diff --git a/src/Kestrel.Core/Internal/HttpConnection.cs b/src/Kestrel.Core/Internal/HttpConnection.cs
index 5673485d77..c53c66d16a 100644
--- a/src/Kestrel.Core/Internal/HttpConnection.cs
+++ b/src/Kestrel.Core/Internal/HttpConnection.cs
@@ -238,10 +238,8 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Internal
             });
         }
 
-        public void OnConnectionClosed(Exception ex)
+        public void OnConnectionClosed()
         {
-            Abort(ex);
-
             _socketClosedTcs.TrySetResult(null);
         }
 
diff --git a/src/Kestrel.Core/Internal/HttpConnectionMiddleware.cs b/src/Kestrel.Core/Internal/HttpConnectionMiddleware.cs
index 598dae82d8..907115dd9a 100644
--- a/src/Kestrel.Core/Internal/HttpConnectionMiddleware.cs
+++ b/src/Kestrel.Core/Internal/HttpConnectionMiddleware.cs
@@ -1,11 +1,12 @@
-using System.Collections.Generic;
+using System;
+using System.Collections.Generic;
 using System.Net;
 using System.Threading;
 using System.Threading.Tasks;
-using Microsoft.AspNetCore.Hosting.Server;
-using Microsoft.AspNetCore.Http.Features;
 using Microsoft.AspNetCore.Connections;
 using Microsoft.AspNetCore.Connections.Features;
+using Microsoft.AspNetCore.Hosting.Server;
+using Microsoft.AspNetCore.Http.Features;
 using Microsoft.AspNetCore.Server.Kestrel.Core.Adapter.Internal;
 using Microsoft.AspNetCore.Server.Kestrel.Transport.Abstractions.Internal;
 
@@ -30,7 +31,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Internal
             _connectionAdapters = adapters;
         }
 
-        public Task OnConnectionAsync(ConnectionContext connectionContext)
+        public async Task OnConnectionAsync(ConnectionContext connectionContext)
         {
             // We need the transport feature so that we can cancel the output reader that the transport is using
             // This is a bit of a hack but it preserves the existing semantics
@@ -69,22 +70,46 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Internal
             }
 
             var connection = new HttpConnection(httpConnectionContext);
+            var inputCompletionState = new PipeCompletionState(connection);
+            var outputCompletionState = new PipeCompletionState(connection);
 
             var processingTask = connection.StartRequestProcessing(_application);
 
-            connectionContext.Transport.Input.OnWriterCompleted((error, state) =>
-            {
-                ((HttpConnection)state).Abort(error);
-            },
-            connection);
+            connectionContext.Transport.Input.OnWriterCompleted(
+                (error, state) => ((PipeCompletionState)state).CompletionCallback(error),
+                inputCompletionState);
 
-            connectionContext.Transport.Output.OnReaderCompleted((error, state) =>
-            {
-                ((HttpConnection)state).OnConnectionClosed(error);
-            },
-            connection);
+            connectionContext.Transport.Output.OnReaderCompleted(
+                (error, state) => ((PipeCompletionState)state).CompletionCallback(error),
+                outputCompletionState);
 
-            return processingTask;
+            await inputCompletionState.CompletionTask;
+            await outputCompletionState.CompletionTask;
+
+            connection.OnConnectionClosed();
+
+            await processingTask;
+        }
+
+        private class PipeCompletionState
+        {
+            private readonly HttpConnection _connection;
+            private readonly TaskCompletionSource<object> _completionTcs = new TaskCompletionSource<object>();
+
+            public PipeCompletionState(HttpConnection connection)
+            {
+                _connection = connection;
+                CompletionTask = _completionTcs.Task;
+            }
+
+
+            public Task CompletionTask { get; }
+
+            public void CompletionCallback(Exception error)
+            {
+                _connection.Abort(error);
+                _completionTcs.SetResult(null);
+            }
         }
     }
 }
diff --git a/test/Kestrel.FunctionalTests/RequestTests.cs b/test/Kestrel.FunctionalTests/RequestTests.cs
index c57c5af39d..568f13e299 100644
--- a/test/Kestrel.FunctionalTests/RequestTests.cs
+++ b/test/Kestrel.FunctionalTests/RequestTests.cs
@@ -1266,7 +1266,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.FunctionalTests
                 }
             };
 
-            var scratchBuffer = new byte[maxRequestBufferSize * 2 + 1];
+            var scratchBuffer = new byte[maxRequestBufferSize * 8];
 
             using (var server = new TestServer(async context =>
             {
diff --git a/test/Kestrel.FunctionalTests/ResponseTests.cs b/test/Kestrel.FunctionalTests/ResponseTests.cs
index f98fa41185..d0d7c4e986 100644
--- a/test/Kestrel.FunctionalTests/ResponseTests.cs
+++ b/test/Kestrel.FunctionalTests/ResponseTests.cs
@@ -2381,7 +2381,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.FunctionalTests
                 }
             };
 
-            var scratchBuffer = new byte[maxRequestBufferSize * 2 + 1];
+            var scratchBuffer = new byte[maxRequestBufferSize * 8];
 
             using (var server = new TestServer(async context =>
             {