diff --git a/Cargo.lock b/Cargo.lock
index aa4ad7ab4f..f582c83cfc 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -1010,6 +1010,7 @@ dependencies = [
  "linkerd-app-core",
  "linkerd-app-test",
  "linkerd-http-access-log",
+ "linkerd-http-metrics",
  "linkerd-idle-cache",
  "linkerd-io",
  "linkerd-meshtls",
diff --git a/linkerd/app/admin/src/stack.rs b/linkerd/app/admin/src/stack.rs
index bb7fd6282d..f703155e63 100644
--- a/linkerd/app/admin/src/stack.rs
+++ b/linkerd/app/admin/src/stack.rs
@@ -99,6 +99,7 @@ impl Config {
         let admin = crate::server::Admin::new(report, ready, shutdown, trace);
         let admin = svc::stack(move |_| admin.clone())
             .push(metrics.proxy.http_endpoint.to_layer::<classify::Response, _, Permitted>())
+            .push(classify::NewClassify::layer_default())
             .push_map_target(|(permit, http)| Permitted { permit, http })
             .push(inbound::policy::NewHttpPolicy::layer(metrics.http_authz.clone()))
             .push(Rescue::layer())
diff --git a/linkerd/app/core/src/control.rs b/linkerd/app/core/src/control.rs
index 9591661071..45b472d221 100644
--- a/linkerd/app/core/src/control.rs
+++ b/linkerd/app/core/src/control.rs
@@ -124,6 +124,7 @@ impl Config {
             .lift_new()
             .push(self::balance::layer(dns, resolve_backoff))
             .push(metrics.to_layer::<classify::Response, _, _>())
+            .push(classify::NewClassify::layer_default())
             // This buffer allows a resolver client to be shared across stacks.
             // No load shed is applied here, however, so backpressure may leak
             // into the caller task.
diff --git a/linkerd/app/inbound/Cargo.toml b/linkerd/app/inbound/Cargo.toml
index 8f74e9635f..c76c1b229d 100644
--- a/linkerd/app/inbound/Cargo.toml
+++ b/linkerd/app/inbound/Cargo.toml
@@ -52,6 +52,7 @@ libfuzzer-sys = { version = "0.4", features = ["arbitrary-derive"] }
 [dev-dependencies]
 hyper = { version = "0.14", features = ["http1", "http2"] }
 linkerd-app-test = { path = "../test" }
+linkerd-http-metrics = { path = "../../http-metrics", features = ["test-util"] }
 linkerd-idle-cache = { path = "../../idle-cache", features = ["test-util"] }
 linkerd-io = { path = "../../io", features = ["tokio-test"] }
 linkerd-meshtls = { path = "../../meshtls", features = ["rustls"] }
diff --git a/linkerd/app/inbound/src/http/router.rs b/linkerd/app/inbound/src/http/router.rs
index 9e895e04f9..a234b86bac 100644
--- a/linkerd/app/inbound/src/http/router.rs
+++ b/linkerd/app/inbound/src/http/router.rs
@@ -148,7 +148,8 @@ impl<C> Inbound<C> {
             // Attempts to discover a service profile for each logical target (as
             // informed by the request's headers). The stack is cached until a
             // request has not been received for `cache_max_idle_age`.
-            let router = http.clone()
+            let router = http
+                .clone()
                 .check_new_service::<Logical, http::Request<http::BoxBody>>()
                 .push_map_target(|p: Profile| p.logical)
                 .push(profiles::http::NewProxyRouter::layer(
@@ -164,6 +165,7 @@ impl<C> Inbound<C> {
                                 .to_layer::<classify::Response, _, _>(),
                         )
                         .push_on_service(http::BoxResponse::layer())
+                        // Configure a per-route response classifier based on the profile.
                         .push(classify::NewClassify::layer())
                         .push_http_insert_target::<profiles::http::Route>()
                         .push_map_target(|(route, profile)| ProfileRoute { route, profile })
@@ -186,10 +188,7 @@ impl<C> Inbound<C> {
                         }
                         Ok(svc::Either::B(logical))
                     },
-                    http.clone()
-                    .push_on_service(svc::MapErr::layer(Error::from))
-                        .check_new_service::<Logical, http::Request<_>>()
-                        .into_inner(),
+                    http.clone().into_inner(),
                 )
                 .check_new_service::<(Option<profiles::Receiver>, Logical), http::Request<_>>();
 
@@ -229,8 +228,7 @@ impl<C> Inbound<C> {
                 // Skip the profile stack if it takes too long to become ready.
                 .push_when_unready(config.profile_skip_timeout, http.into_inner())
                 .push_on_service(
-                    svc::layers()
-                        .push(rt.metrics.proxy.stack.layer(stack_labels("http", "logical")))
+                    rt.metrics.proxy.stack.layer(stack_labels("http", "logical")),
                 )
                 .push(svc::NewQueue::layer_via(config.http_request_queue))
                 .push_new_idle_cached(config.discovery_idle_timeout)
@@ -239,6 +237,9 @@ impl<C> Inbound<C> {
                         .push(http::Retain::layer())
                         .push(http::BoxResponse::layer()),
                 )
+                // Configure default response classification early. It may be
+                // overridden by profile routes above.
+                .push(classify::NewClassify::layer_default())
                 .check_new_service::<Logical, http::Request<http::BoxBody>>()
                 .instrument(|t: &Logical| {
                     let name = t.logical.as_ref().map(tracing::field::display);
@@ -414,12 +415,6 @@ impl Param<metrics::EndpointLabels> for Logical {
     }
 }
 
-impl Param<classify::Request> for Logical {
-    fn param(&self) -> classify::Request {
-        classify::Request::default()
-    }
-}
-
 impl tap::Inspect for Logical {
     fn src_addr<B>(&self, req: &http::Request<B>) -> Option<SocketAddr> {
         req.extensions().get::<Remote<ClientAddr>>().map(|a| **a)
diff --git a/linkerd/app/inbound/src/http/tests.rs b/linkerd/app/inbound/src/http/tests.rs
index cf55c435bc..d21f005af5 100644
--- a/linkerd/app/inbound/src/http/tests.rs
+++ b/linkerd/app/inbound/src/http/tests.rs
@@ -6,10 +6,11 @@ use crate::{
     },
     Config, Inbound,
 };
-use hyper::{client::conn::Builder as ClientBuilder, Body, Request, Response};
+use hyper::{body::HttpBody, client::conn::Builder as ClientBuilder, Body, Request, Response};
 use linkerd_app_core::{
+    classify,
     errors::respond::L5D_PROXY_ERROR,
-    identity, io,
+    identity, io, metrics,
     proxy::http,
     svc::{self, NewService, Param},
     tls,
@@ -19,6 +20,7 @@ use linkerd_app_core::{
 use linkerd_app_test::connect::ConnectFuture;
 use linkerd_tracing::test::trace_init;
 use std::{net::SocketAddr, sync::Arc};
+use tokio::time;
 use tracing::Instrument;
 
 fn build_server<I>(
@@ -469,6 +471,84 @@ async fn grpc_unmeshed_response_error_header() {
     let _ = bg.await;
 }
 
+#[tokio::test(flavor = "current_thread")]
+async fn grpc_response_class() {
+    let _trace = trace_init();
+
+    // Build a mock connector serves a gRPC server that returns errors.
+    let connect = {
+        let mut server = hyper::server::conn::Http::new();
+        server.http2_only(true);
+        support::connect().endpoint_fn_boxed(
+            Target::addr(),
+            grpc_status_server(server, tonic::Code::Unknown),
+        )
+    };
+
+    // Build a client using the connect that always errors.
+    let mut client = ClientBuilder::new();
+    client.http2_only(true);
+    let profiles = profile::resolver();
+    let profile_tx =
+        profiles.profile_tx(NameAddr::from_str_and_port("foo.svc.cluster.local", 5550).unwrap());
+    profile_tx.send(profile::Profile::default()).unwrap();
+    let cfg = default_config();
+    let (rt, _shutdown) = runtime();
+    let metrics = rt
+        .metrics
+        .clone()
+        .http_endpoint
+        .into_report(time::Duration::from_secs(3600));
+    let server = build_server(cfg, rt, profiles, connect).new_service(Target::meshed_h2());
+    let (mut client, bg) = http_util::connect_and_accept(&mut client, server).await;
+
+    // Send a request and assert that it is OK with the expected header
+    // message.
+    let req = Request::builder()
+        .method(http::Method::POST)
+        .uri("http://foo.svc.cluster.local:5550")
+        .header(http::header::CONTENT_TYPE, "application/grpc")
+        .body(Body::default())
+        .unwrap();
+
+    let mut response = http_util::http_request(&mut client, req).await.unwrap();
+    assert_eq!(response.status(), http::StatusCode::OK);
+
+    response.body_mut().data().await;
+    let trls = response.body_mut().trailers().await.unwrap().unwrap();
+    assert_eq!(trls.get("grpc-status").unwrap().to_str().unwrap(), "2");
+
+    let response_total = metrics
+        .get_response_total(
+            &metrics::EndpointLabels::Inbound(metrics::InboundEndpointLabels {
+                tls: Target::meshed_h2().1,
+                authority: Some("foo.svc.cluster.local:5550".parse().unwrap()),
+                target_addr: "127.0.0.1:80".parse().unwrap(),
+                policy: metrics::RouteAuthzLabels {
+                    route: metrics::RouteLabels {
+                        server: metrics::ServerLabel(Arc::new(policy::Meta::Resource {
+                            group: "policy.linkerd.io".into(),
+                            kind: "server".into(),
+                            name: "testsrv".into(),
+                        })),
+                        route: policy::Meta::new_default("default"),
+                    },
+                    authz: Arc::new(policy::Meta::Resource {
+                        group: "policy.linkerd.io".into(),
+                        kind: "serverauthorization".into(),
+                        name: "testsaz".into(),
+                    }),
+                },
+            }),
+            Some(http::StatusCode::OK),
+            &classify::Class::Grpc(Err(tonic::Code::Unknown)),
+        )
+        .expect("response_total not found");
+    assert_eq!(response_total, 1.0);
+
+    drop((client, bg));
+}
+
 #[tracing::instrument]
 fn hello_server(
     http: hyper::server::conn::Http,
@@ -490,6 +570,42 @@ fn hello_server(
     }
 }
 
+#[tracing::instrument]
+fn grpc_status_server(
+    http: hyper::server::conn::Http,
+    status: tonic::Code,
+) -> impl Fn(Remote<ServerAddr>) -> io::Result<io::BoxedIo> {
+    move |endpoint| {
+        let span = tracing::info_span!("grpc_status_server", ?endpoint);
+        let _e = span.enter();
+        tracing::info!("mock connecting");
+        let (client_io, server_io) = support::io::duplex(4096);
+        tokio::spawn(
+            http.serve_connection(
+                server_io,
+                hyper::service::service_fn(move |request: Request<Body>| async move {
+                    tracing::info!(?request);
+                    let (mut tx, rx) = Body::channel();
+                    tokio::spawn(async move {
+                        let mut trls = ::http::HeaderMap::new();
+                        trls.insert("grpc-status", (status as u32).to_string().parse().unwrap());
+                        tx.send_trailers(trls).await
+                    });
+                    Ok::<_, io::Error>(
+                        http::Response::builder()
+                            .version(::http::Version::HTTP_2)
+                            .header("content-type", "application/grpc")
+                            .body(rx)
+                            .unwrap(),
+                    )
+                }),
+            )
+            .in_current_span(),
+        );
+        Ok(io::BoxedIo::new(client_io))
+    }
+}
+
 #[tracing::instrument]
 fn connect_error() -> impl Fn(Remote<ServerAddr>) -> io::Result<io::BoxedIo> {
     move |_| {
@@ -523,7 +639,7 @@ fn connect_timeout(
 struct Target(http::Version, tls::ConditionalServerTls);
 
 #[track_caller]
-fn check_error_header(hdrs: &hyper::header::HeaderMap, expected: &str) {
+fn check_error_header(hdrs: &::http::HeaderMap, expected: &str) {
     let message = hdrs
         .get(L5D_PROXY_ERROR)
         .expect("response did not contain l5d-proxy-error header")
diff --git a/linkerd/app/outbound/src/http/endpoint/tests.rs b/linkerd/app/outbound/src/http/endpoint/tests.rs
index 461ea2e913..863e4a1147 100644
--- a/linkerd/app/outbound/src/http/endpoint/tests.rs
+++ b/linkerd/app/outbound/src/http/endpoint/tests.rs
@@ -27,6 +27,8 @@ async fn http11_forward() {
         .with_stack(connect)
         .push_http_tcp_client()
         .push_http_endpoint::<_, http::BoxBody, _>()
+        .into_stack()
+        .push(classify::NewClassify::layer_default())
         .into_inner();
 
     let svc = stack.new_service(Endpoint {
@@ -61,6 +63,8 @@ async fn http2_forward() {
         .with_stack(connect)
         .push_http_tcp_client()
         .push_http_endpoint::<_, http::BoxBody, _>()
+        .into_stack()
+        .push(classify::NewClassify::layer_default())
         .into_inner();
 
     let svc = stack.new_service(Endpoint {
@@ -97,6 +101,8 @@ async fn orig_proto_upgrade() {
         .with_stack(connect)
         .push_http_tcp_client()
         .push_http_endpoint::<_, http::BoxBody, _>()
+        .into_stack()
+        .push(classify::NewClassify::layer_default())
         .into_inner();
 
     let svc = stack.new_service(Endpoint {
@@ -146,6 +152,7 @@ async fn orig_proto_skipped_on_http_upgrade() {
         .push_http_tcp_client()
         .push_http_endpoint::<_, http::BoxBody, _>()
         .into_stack()
+        .push(classify::NewClassify::layer_default())
         .push_on_service(http::BoxRequest::layer())
         // We need the server-side upgrade layer to annotate the request so that the client
         // knows that an HTTP upgrade is in progress.
@@ -192,6 +199,8 @@ async fn orig_proto_http2_noop() {
         .with_stack(connect)
         .push_http_tcp_client()
         .push_http_endpoint::<_, http::BoxBody, _>()
+        .into_stack()
+        .push(classify::NewClassify::layer_default())
         .into_inner();
 
     let svc = stack.new_service(Endpoint {
diff --git a/linkerd/app/outbound/src/http/retry.rs b/linkerd/app/outbound/src/http/retry.rs
index b61ddf3722..625ff19648 100644
--- a/linkerd/app/outbound/src/http/retry.rs
+++ b/linkerd/app/outbound/src/http/retry.rs
@@ -131,6 +131,10 @@ where
             clone.extensions_mut().insert(client_handle);
         }
 
+        if let Some(classify) = req.extensions().get::<classify::Response>().cloned() {
+            clone.extensions_mut().insert(classify);
+        }
+
         Some(clone)
     }
 }
diff --git a/linkerd/http-metrics/Cargo.toml b/linkerd/http-metrics/Cargo.toml
index 61c7eeda72..3c22bc329e 100644
--- a/linkerd/http-metrics/Cargo.toml
+++ b/linkerd/http-metrics/Cargo.toml
@@ -6,6 +6,9 @@ license = "Apache-2.0"
 edition = "2021"
 publish = false
 
+[features]
+test-util = []
+
 [dependencies]
 bytes = "1"
 futures = { version = "0.3", default-features = false }
diff --git a/linkerd/http-metrics/src/lib.rs b/linkerd/http-metrics/src/lib.rs
index c28376a0b8..c33922b845 100644
--- a/linkerd/http-metrics/src/lib.rs
+++ b/linkerd/http-metrics/src/lib.rs
@@ -25,6 +25,22 @@ where
     include_latencies: bool,
 }
 
+#[cfg(feature = "test-util")]
+impl<T: Hash + Eq, C: Hash + Eq> Report<T, requests::Metrics<C>> {
+    pub fn get_response_total(
+        &self,
+        labels: &T,
+        status: Option<http::StatusCode>,
+        class: &C,
+    ) -> Option<f64> {
+        let registry = self.registry.lock();
+        let requests = registry.get(labels)?.lock();
+        let status = requests.by_status().get(&status)?;
+        let class = status.by_class().get(class)?;
+        Some(class.total())
+    }
+}
+
 impl<T: Hash + Eq, M> Clone for Report<T, M> {
     fn clone(&self) -> Self {
         Self {
diff --git a/linkerd/http-metrics/src/requests.rs b/linkerd/http-metrics/src/requests.rs
index ca563e6cfa..7a0df94b87 100644
--- a/linkerd/http-metrics/src/requests.rs
+++ b/linkerd/http-metrics/src/requests.rs
@@ -28,7 +28,7 @@ where
 }
 
 #[derive(Debug)]
-struct StatusMetrics<C>
+pub struct StatusMetrics<C>
 where
     C: Hash + Eq,
 {
@@ -87,6 +87,17 @@ impl<C: Hash + Eq> Default for Metrics<C> {
     }
 }
 
+#[cfg(feature = "test-util")]
+impl<C: Hash + Eq> Metrics<C> {
+    pub fn total(&self) -> &Counter {
+        &self.total
+    }
+
+    pub fn by_status(&self) -> &HashMap<Option<http::StatusCode>, StatusMetrics<C>> {
+        &self.by_status
+    }
+}
+
 impl<C: Hash + Eq> LastUpdate for Metrics<C> {
     fn last_update(&self) -> Instant {
         self.last_update
@@ -105,6 +116,20 @@ where
     }
 }
 
+#[cfg(feature = "test-util")]
+impl<C: Hash + Eq> StatusMetrics<C> {
+    pub fn by_class(&self) -> &HashMap<C, ClassMetrics> {
+        &self.by_class
+    }
+}
+
+#[cfg(feature = "test-util")]
+impl ClassMetrics {
+    pub fn total(&self) -> f64 {
+        self.total.value()
+    }
+}
+
 #[cfg(test)]
 mod tests {
     #[test]
diff --git a/linkerd/http-metrics/src/requests/service.rs b/linkerd/http-metrics/src/requests/service.rs
index 71a75c5860..279117f3b8 100644
--- a/linkerd/http-metrics/src/requests/service.rs
+++ b/linkerd/http-metrics/src/requests/service.rs
@@ -96,7 +96,7 @@ where
 impl<S, C> Clone for HttpMetrics<S, C>
 where
     S: Clone,
-    C: ClassifyResponse + Clone + Default + Send + Sync + 'static,
+    C: ClassifyResponse + Clone + Send + Sync + 'static,
     C::Class: Hash + Eq,
 {
     fn clone(&self) -> Self {
@@ -108,6 +108,16 @@ where
     }
 }
 
+#[inline]
+fn classify_unwrap_if_debug_else_default<C, B>(req: &http::Request<B>) -> C
+where
+    C: Clone + Default + Send + Sync + 'static,
+{
+    let c = req.extensions().get::<C>().cloned();
+    debug_assert!(c.is_some(), "request must have response classifier");
+    c.unwrap_or_default()
+}
+
 impl<C, P, S, A, B> Proxy<http::Request<A>, S> for HttpMetrics<P, C>
 where
     P: Proxy<http::Request<RequestBody<A, C::Class>>, S, Response = http::Response<B>>,
@@ -143,10 +153,8 @@ where
             http::Request::from_parts(head, body)
         };
 
-        let classify = req.extensions().get::<C>().cloned().unwrap_or_default();
-
         ResponseFuture {
-            classify: Some(classify),
+            classify: Some(classify_unwrap_if_debug_else_default(&req)),
             metrics: self.metrics.clone(),
             stream_open_at: Instant::now(),
             inner: self.inner.proxy(svc, req),
@@ -167,6 +175,7 @@ where
     type Error = Error;
     type Future = ResponseFuture<S::Future, C>;
 
+    #[inline]
     fn poll_ready(&mut self, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
         self.inner.poll_ready(cx).map_err(Into::into)
     }
@@ -192,10 +201,8 @@ where
             http::Request::from_parts(head, body)
         };
 
-        let classify = req.extensions().get::<C>().cloned().unwrap_or_default();
-
         ResponseFuture {
-            classify: Some(classify),
+            classify: Some(classify_unwrap_if_debug_else_default(&req)),
             metrics: self.metrics.clone(),
             stream_open_at: Instant::now(),
             inner: self.inner.call(req),
diff --git a/linkerd/proxy/http/src/classify/insert.rs b/linkerd/proxy/http/src/classify/insert.rs
index ba67096dea..958f507863 100644
--- a/linkerd/proxy/http/src/classify/insert.rs
+++ b/linkerd/proxy/http/src/classify/insert.rs
@@ -1,4 +1,4 @@
-use linkerd_stack::{layer, ExtractParam, NewService, Proxy, Service};
+use linkerd_stack::{layer, CloneParam, ExtractParam, NewService, Proxy, Service};
 use std::{
     marker::PhantomData,
     task::{Context, Poll},
@@ -33,6 +33,12 @@ impl<C, N> NewInsertClassifyResponse<C, (), N> {
     }
 }
 
+impl<C: Clone + Default, N> NewInsertClassifyResponse<C, CloneParam<C>, N> {
+    pub fn layer_default() -> impl layer::Layer<N, Service = Self> + Clone {
+        Self::layer_via(CloneParam::from(C::default()))
+    }
+}
+
 impl<T, C, X, N> NewService<T> for NewInsertClassifyResponse<C, X, N>
 where
     C: super::Classify,
@@ -61,8 +67,9 @@ where
 
     fn proxy(&self, svc: &mut S, mut req: http::Request<B>) -> Self::Future {
         let classify_rsp = self.classify.classify(&req);
-        let prior = req.extensions_mut().insert(classify_rsp);
-        debug_assert!(prior.is_none(), "classification extension already existed");
+        if req.extensions_mut().insert(classify_rsp).is_some() {
+            tracing::debug!("Overrode response classifier");
+        }
         self.inner.proxy(svc, req)
     }
 }
@@ -83,8 +90,9 @@ where
 
     fn call(&mut self, mut req: http::Request<B>) -> Self::Future {
         let classify_rsp = self.classify.classify(&req);
-        let prior = req.extensions_mut().insert(classify_rsp);
-        debug_assert!(prior.is_none(), "classification extension already existed");
+        if req.extensions_mut().insert(classify_rsp).is_some() {
+            tracing::debug!("Overrode response classifier");
+        }
         self.inner.call(req)
     }
 }