diff --git a/src/body/body.rs b/src/body/body.rs
index 111867a5ed..9164320a0a 100644
--- a/src/body/body.rs
+++ b/src/body/body.rs
@@ -323,7 +323,12 @@ impl Body {
                     ping.record_data(bytes.len());
                     Poll::Ready(Some(Ok(bytes)))
                 }
-                Some(Err(e)) => Poll::Ready(Some(Err(crate::Error::new_body(e)))),
+                Some(Err(e)) => match e.reason() {
+                    // These reasons should cause stop of body reading, but nor fail it.
+                    // The same logic as for `AsyncRead for H2Upgraded` is applied here.
+                    Some(h2::Reason::NO_ERROR) | Some(h2::Reason::CANCEL) => Poll::Ready(None),
+                    _ => Poll::Ready(Some(Err(crate::Error::new_body(e)))),
+                },
                 None => Poll::Ready(None),
             },
 
diff --git a/src/proto/mod.rs b/src/proto/mod.rs
index f938bf532b..3628576dc1 100644
--- a/src/proto/mod.rs
+++ b/src/proto/mod.rs
@@ -50,7 +50,7 @@ pub(crate) enum BodyLength {
     Unknown,
 }
 
-/// Status of when a Disaptcher future completes.
+/// Status of when a Dispatcher future completes.
 pub(crate) enum Dispatched {
     /// Dispatcher completely shutdown connection.
     Shutdown,
diff --git a/tests/client.rs b/tests/client.rs
index 2953313798..88fcd3a564 100644
--- a/tests/client.rs
+++ b/tests/client.rs
@@ -3154,6 +3154,61 @@ mod conn {
             .expect("client should be open");
     }
 
+    #[tokio::test]
+    async fn http2_responds_before_consuming_request_body() {
+        // Test that a early-response from server works correctly (request body wasn't fully consumed).
+        // https://github.com/hyperium/hyper/issues/2872
+        use hyper::service::service_fn;
+
+        let _ = pretty_env_logger::try_init();
+
+        let listener = TkTcpListener::bind(SocketAddr::from(([127, 0, 0, 1], 0)))
+            .await
+            .unwrap();
+        let addr = listener.local_addr().unwrap();
+
+        // Spawn an HTTP2 server that responds before reading the whole request body.
+        // It's normal case to decline the request due to headers or size of the body.
+        tokio::spawn(async move {
+            let sock = listener.accept().await.unwrap().0;
+            hyper::server::conn::Http::new()
+                .http2_only(true)
+                .serve_connection(
+                    sock,
+                    service_fn(|_req| async move {
+                        Ok::<_, hyper::Error>(http::Response::new(hyper::Body::from(
+                            "No bread for you!",
+                        )))
+                    }),
+                )
+                .await
+                .expect("serve_connection");
+        });
+
+        let io = tcp_connect(&addr).await.expect("tcp connect");
+        let (mut client, conn) = conn::Builder::new()
+            .http2_only(true)
+            .handshake::<_, Body>(io)
+            .await
+            .expect("http handshake");
+
+        tokio::spawn(async move {
+            conn.await.expect("client conn shouldn't error");
+        });
+
+        // Use a channel to keep request stream open
+        let (_tx, body) = hyper::Body::channel();
+        let req = Request::post("/a").body(body).unwrap();
+        let resp = client.send_request(req).await.expect("send_request");
+        assert!(resp.status().is_success());
+
+        let body = hyper::body::to_bytes(resp.into_body())
+            .await
+            .expect("get response body with no error");
+
+        assert_eq!(body.as_ref(), b"No bread for you!");
+    }
+
     #[tokio::test]
     async fn h2_connect() {
         let _ = pretty_env_logger::try_init();