diff --git a/src/Kestrel.Transport.Sockets/Internal/SocketConnection.cs b/src/Kestrel.Transport.Sockets/Internal/SocketConnection.cs
index cf128c05f3..2ab964e894 100644
--- a/src/Kestrel.Transport.Sockets/Internal/SocketConnection.cs
+++ b/src/Kestrel.Transport.Sockets/Internal/SocketConnection.cs
@@ -57,13 +57,14 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Transport.Sockets.Internal
 
         public async Task StartAsync(IConnectionHandler connectionHandler)
         {
+            Exception sendError = null;
             try
             {
                 connectionHandler.OnConnection(this);
 
                 // Spawn send and receive logic
                 Task receiveTask = DoReceive();
-                Task sendTask = DoSend();
+                Task<Exception> sendTask = DoSend();
 
                 // If the sending task completes then close the receive
                 // We don't need to do this in the other direction because the kestrel
@@ -76,7 +77,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Transport.Sockets.Internal
 
                 // Now wait for both to complete
                 await receiveTask;
-                await sendTask;
+                sendError = await sendTask;
 
                 // Dispose the socket(should noop if already called)
                 _socket.Dispose();
@@ -85,6 +86,11 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Transport.Sockets.Internal
             {
                 _trace.LogError(0, ex, $"Unexpected exception in {nameof(SocketConnection)}.{nameof(StartAsync)}.");
             }
+            finally
+            {
+                // Complete the output after disposing the socket
+                Output.Complete(sendError);
+            }
         }
 
         private async Task DoReceive()
@@ -181,7 +187,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Transport.Sockets.Internal
             }
         }
 
-        private async Task DoSend()
+        private async Task<Exception> DoSend()
         {
             Exception error = null;
 
@@ -233,8 +239,6 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Transport.Sockets.Internal
             }
             finally
             {
-                Output.Complete(error);
-
                 // Make sure to close the connection only after the _aborted flag is set.
                 // Without this, the RequestsCanBeAbortedMidRead test will sometimes fail when
                 // a BadHttpRequestException is thrown instead of a TaskCanceledException.
@@ -242,6 +246,8 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Transport.Sockets.Internal
                 _trace.ConnectionWriteFin(ConnectionId);
                 _socket.Shutdown(SocketShutdown.Both);
             }
+
+            return error;
         }
     }
 }