diff --git a/src/Servers/Kestrel/Core/src/Internal/Http2/Http2FrameWriter.cs b/src/Servers/Kestrel/Core/src/Internal/Http2/Http2FrameWriter.cs
index 630927bb3ff6..593408337142 100644
--- a/src/Servers/Kestrel/Core/src/Internal/Http2/Http2FrameWriter.cs
+++ b/src/Servers/Kestrel/Core/src/Internal/Http2/Http2FrameWriter.cs
@@ -89,7 +89,6 @@ public void Complete()
 
                 _completed = true;
                 _connectionOutputFlowControl.Abort();
-                _outputWriter.Complete();
             }
         }
 
diff --git a/src/Servers/Kestrel/Core/src/Middleware/HttpsConnectionMiddleware.cs b/src/Servers/Kestrel/Core/src/Middleware/HttpsConnectionMiddleware.cs
index 2449fc514629..7c34e025c6e8 100644
--- a/src/Servers/Kestrel/Core/src/Middleware/HttpsConnectionMiddleware.cs
+++ b/src/Servers/Kestrel/Core/src/Middleware/HttpsConnectionMiddleware.cs
@@ -103,7 +103,10 @@ private async Task InnerOnConnectionAsync(ConnectionContext context)
 
             if (_options.ClientCertificateMode == ClientCertificateMode.NoCertificate)
             {
-                sslDuplexPipe = new SslDuplexPipe(context.Transport, inputPipeOptions, outputPipeOptions);
+                sslDuplexPipe = new SslDuplexPipe(context.Transport, inputPipeOptions, outputPipeOptions)
+                {
+                    Log = _logger
+                };
                 certificateRequired = false;
             }
             else
@@ -140,7 +143,10 @@ private async Task InnerOnConnectionAsync(ConnectionContext context)
                         }
 
                         return true;
-                    }));
+                    }))
+                {
+                    Log = _logger
+                };
 
                 certificateRequired = true;
             }
diff --git a/src/Servers/Kestrel/Core/src/Middleware/Internal/DuplexPipeStreamAdapter.cs b/src/Servers/Kestrel/Core/src/Middleware/Internal/DuplexPipeStreamAdapter.cs
index 5b5cc019057c..0a0d09384c21 100644
--- a/src/Servers/Kestrel/Core/src/Middleware/Internal/DuplexPipeStreamAdapter.cs
+++ b/src/Servers/Kestrel/Core/src/Middleware/Internal/DuplexPipeStreamAdapter.cs
@@ -5,6 +5,7 @@
 using System.IO;
 using System.IO.Pipelines;
 using System.Threading.Tasks;
+using Microsoft.Extensions.Logging;
 
 namespace Microsoft.AspNetCore.Server.Kestrel.Core.Internal
 {
@@ -14,36 +15,114 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Internal
     /// <typeparam name="TStream"></typeparam>
     internal class DuplexPipeStreamAdapter<TStream> : DuplexPipeStream, IDuplexPipe where TStream : Stream
     {
+        private readonly Pipe _output;
+        private Task _outputTask;
+
         public DuplexPipeStreamAdapter(IDuplexPipe duplexPipe, Func<Stream, TStream> createStream) :
             this(duplexPipe, new StreamPipeReaderOptions(leaveOpen: true), new StreamPipeWriterOptions(leaveOpen: true), createStream)
         {
         }
 
-        public DuplexPipeStreamAdapter(IDuplexPipe duplexPipe, StreamPipeReaderOptions readerOptions, StreamPipeWriterOptions writerOptions, Func<Stream, TStream> createStream) : base(duplexPipe.Input, duplexPipe.Output)
+        public DuplexPipeStreamAdapter(IDuplexPipe duplexPipe, StreamPipeReaderOptions readerOptions, StreamPipeWriterOptions writerOptions, Func<Stream, TStream> createStream) :
+            base(duplexPipe.Input, duplexPipe.Output)
         {
             Stream = createStream(this);
+
+            var outputOptions = new PipeOptions(pool: writerOptions.Pool,
+                                                readerScheduler: PipeScheduler.Inline,
+                                                writerScheduler: PipeScheduler.Inline,
+                                                pauseWriterThreshold: 1,
+                                                resumeWriterThreshold: 1,
+                                                minimumSegmentSize: writerOptions.MinimumBufferSize,
+                                                useSynchronizationContext: false);
+
             Input = PipeReader.Create(Stream, readerOptions);
-            Output = PipeWriter.Create(Stream, writerOptions);
+
+            // We're using a pipe here because the HTTP/2 stack in Kestrel currently makes assumptions
+            // about when it is ok to write to the PipeWriter. This should be reverted back to PipeWriter.Create once
+            // those patterns are fixed.
+            _output = new Pipe(outputOptions);
         }
 
+        public ILogger Log { get; set; }
+
         public TStream Stream { get; }
 
         public PipeReader Input { get; }
 
-        public PipeWriter Output { get; }
+        public PipeWriter Output
+        {
+            get
+            {
+                if (_outputTask == null)
+                {
+                    _outputTask = WriteOutputAsync();
+                }
 
-        protected override void Dispose(bool disposing)
+                return _output.Writer;
+            }
+        }
+
+        public override async ValueTask DisposeAsync()
         {
             Input.Complete();
-            Output.Complete();
-            base.Dispose(disposing);
+            _output.Writer.Complete();
+
+            if (_outputTask != null)
+            {
+                // Wait for the output task to complete, this ensures that we've copied
+                // the application data to the underlying stream
+                await _outputTask;
+            }
         }
 
-        public override ValueTask DisposeAsync()
+        private async Task WriteOutputAsync()
         {
-            Input.Complete();
-            Output.Complete();
-            return base.DisposeAsync();
+            try
+            {
+                while (true)
+                {
+                    var result = await _output.Reader.ReadAsync();
+                    var buffer = result.Buffer;
+
+                    try
+                    {
+                        if (buffer.IsEmpty)
+                        {
+                            if (result.IsCompleted)
+                            {
+                                break;
+                            }
+
+                            await Stream.FlushAsync();
+                        }
+                        else if (buffer.IsSingleSegment)
+                        {
+                            await Stream.WriteAsync(buffer.First);
+                        }
+                        else
+                        {
+                            foreach (var memory in buffer)
+                            {
+                                await Stream.WriteAsync(memory);
+                            }
+                        }
+                    }
+                    finally
+                    {
+                        _output.Reader.AdvanceTo(buffer.End);
+                    }
+                }
+            }
+            catch (Exception ex)
+            {
+                Log?.LogCritical(0, ex, $"{GetType().Name}.{nameof(WriteOutputAsync)}");
+            }
+            finally
+            {
+                _output.Reader.Complete();
+            }
         }
     }
 }
+
diff --git a/src/Servers/Kestrel/Core/src/Middleware/LoggingConnectionMiddleware.cs b/src/Servers/Kestrel/Core/src/Middleware/LoggingConnectionMiddleware.cs
index ed9ffb819c7b..5ce9f6df510f 100644
--- a/src/Servers/Kestrel/Core/src/Middleware/LoggingConnectionMiddleware.cs
+++ b/src/Servers/Kestrel/Core/src/Middleware/LoggingConnectionMiddleware.cs
@@ -44,6 +44,7 @@ private class LoggingDuplexPipe : DuplexPipeStreamAdapter<LoggingStream>
             public LoggingDuplexPipe(IDuplexPipe transport, ILogger logger) :
                 base(transport, stream => new LoggingStream(stream, logger))
             {
+                Log = logger;
             }
         }
     }
diff --git a/src/Servers/Kestrel/test/InMemory.FunctionalTests/Http2/Http2TestBase.cs b/src/Servers/Kestrel/test/InMemory.FunctionalTests/Http2/Http2TestBase.cs
index 543a9dc2896b..d9fd7fe6f52f 100644
--- a/src/Servers/Kestrel/test/InMemory.FunctionalTests/Http2/Http2TestBase.cs
+++ b/src/Servers/Kestrel/test/InMemory.FunctionalTests/Http2/Http2TestBase.cs
@@ -467,7 +467,22 @@ protected async Task InitializeConnectionAsync(RequestDelegate application, int
                 CreateConnection();
             }
 
-            _connectionTask = _connection.ProcessRequestsAsync(new DummyApplication(application));
+            var connectionTask = _connection.ProcessRequestsAsync(new DummyApplication(application));
+
+            async Task CompletePipeOnTaskCompletion()
+            {
+                try
+                {
+                    await connectionTask;
+                }
+                finally
+                {
+                    _pair.Transport.Input.Complete();
+                    _pair.Transport.Output.Complete();
+                }
+            }
+
+            _connectionTask = CompletePipeOnTaskCompletion();
 
             await SendPreambleAsync().ConfigureAwait(false);
             await SendSettingsAsync();