diff --git a/src/Microsoft.AspNetCore.Http.Connections/Internal/HttpConnectionDispatcher.cs b/src/Microsoft.AspNetCore.Http.Connections/Internal/HttpConnectionDispatcher.cs
index d66c8ae8b3..24e0090986 100644
--- a/src/Microsoft.AspNetCore.Http.Connections/Internal/HttpConnectionDispatcher.cs
+++ b/src/Microsoft.AspNetCore.Http.Connections/Internal/HttpConnectionDispatcher.cs
@@ -218,8 +218,18 @@ namespace Microsoft.AspNetCore.Http.Connections.Internal
                         // Cancel the previous request
                         connection.Cancellation?.Cancel();
 
-                        // Always wait for the previous request to drain
-                        await connection.PreviousPollTask;
+                        try
+                        {
+                            // Wait for the previous request to drain
+                            await connection.PreviousPollTask;
+                        }
+                        catch (OperationCanceledException)
+                        {
+                            // Previous poll canceled due to connection closing, close this poll too
+                            context.Response.ContentType = "text/plain";
+                            context.Response.StatusCode = StatusCodes.Status204NoContent;
+                            return;
+                        }
 
                         connection.PreviousPollTask = currentRequestTcs.Task;
                     }
@@ -289,6 +299,9 @@ namespace Microsoft.AspNetCore.Http.Connections.Internal
                         // If the status code is a 204 it means the connection is done
                         if (context.Response.StatusCode == StatusCodes.Status204NoContent)
                         {
+                            // Cancel current request to release any waiting poll and let dispose aquire the lock
+                            currentRequestTcs.TrySetCanceled();
+
                             // We should be able to safely dispose because there's no more data being written
                             // We don't need to wait for close here since we've already waited for both sides
                             await _manager.DisposeAndRemoveAsync(connection, closeGracefully: false);
@@ -299,6 +312,9 @@ namespace Microsoft.AspNetCore.Http.Connections.Internal
                     }
                     else if (resultTask.IsFaulted)
                     {
+                        // Cancel current request to release any waiting poll and let dispose aquire the lock
+                        currentRequestTcs.TrySetCanceled();
+
                         // transport task was faulted, we should remove the connection
                         await _manager.DisposeAndRemoveAsync(connection, closeGracefully: false);