diff --git a/src/Microsoft.AspNetCore.Server.Kestrel/Internal/Http/Connection.cs b/src/Microsoft.AspNetCore.Server.Kestrel/Internal/Http/Connection.cs
index 2ba693ef73..9c9e225a9f 100644
--- a/src/Microsoft.AspNetCore.Server.Kestrel/Internal/Http/Connection.cs
+++ b/src/Microsoft.AspNetCore.Server.Kestrel/Internal/Http/Connection.cs
@@ -135,7 +135,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Internal.Http
 
         public Task StopAsync()
         {
-            _frame.Stop();
+            _frame.StopAsync();
             _frame.SocketInput.CompleteAwaiting();
 
             return _socketClosedTcs.Task;
@@ -156,7 +156,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Internal.Http
         {
             if (_filteredStreamAdapter != null)
             {
-                _readInputTask.ContinueWith((task, state) =>
+                Task.WhenAll(_readInputTask, _frame.StopAsync()).ContinueWith((task, state) =>
                 {
                     var connection = (Connection)state;
                     connection._filterContext.Connection.Dispose();
diff --git a/src/Microsoft.AspNetCore.Server.Kestrel/Internal/Http/Frame.cs b/src/Microsoft.AspNetCore.Server.Kestrel/Internal/Http/Frame.cs
index 9a13ab2cb7..f85940605c 100644
--- a/src/Microsoft.AspNetCore.Server.Kestrel/Internal/Http/Frame.cs
+++ b/src/Microsoft.AspNetCore.Server.Kestrel/Internal/Http/Frame.cs
@@ -365,7 +365,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Internal.Http
                     this,
                     default(CancellationToken),
                     TaskCreationOptions.DenyChildAttach,
-                    TaskScheduler.Default);
+                    TaskScheduler.Default).Unwrap();
         }
 
         /// <summary>
@@ -374,7 +374,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Internal.Http
         /// Stop will be called on all active connections, and Task.WaitAll() will be called on every
         /// return value.
         /// </summary>
-        public Task Stop()
+        public Task StopAsync()
         {
             if (!_requestProcessingStopping)
             {
diff --git a/test/Microsoft.AspNetCore.Server.Kestrel.FunctionalTests/HttpsTests.cs b/test/Microsoft.AspNetCore.Server.Kestrel.FunctionalTests/HttpsTests.cs
index 716c71e7b0..8f3a624406 100644
--- a/test/Microsoft.AspNetCore.Server.Kestrel.FunctionalTests/HttpsTests.cs
+++ b/test/Microsoft.AspNetCore.Server.Kestrel.FunctionalTests/HttpsTests.cs
@@ -105,7 +105,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.FunctionalTests
                     {
                         try
                         {
-                            await httpContext.Response.WriteAsync($"hello, world\r\r", ct);
+                            await httpContext.Response.WriteAsync($"hello, world", ct);
                             await Task.Delay(1000, ct);
                         }
                         catch (TaskCanceledException)
@@ -136,6 +136,54 @@ namespace Microsoft.AspNetCore.Server.Kestrel.FunctionalTests
             Assert.False(loggerFactory.ErrorLogger.ObjectDisposedExceptionLogged);
         }
 
+        [Fact]
+        public async Task DoesNotThrowObjectDisposedExceptionFromWriteAsyncAfterConnectionIsAborted()
+        {
+            var tcs = new TaskCompletionSource<object>();
+            var x509Certificate2 = new X509Certificate2(@"TestResources/testCert.pfx", "testPassword");
+            var loggerFactory = new HandshakeErrorLoggerFactory();
+            var hostBuilder = new WebHostBuilder()
+                .UseKestrel(options =>
+                {
+                    options.UseHttps(@"TestResources/testCert.pfx", "testPassword");
+                })
+                .UseUrls("https://127.0.0.1:0/")
+                .UseLoggerFactory(loggerFactory)
+                .Configure(app => app.Run(async httpContext =>
+                {
+                    httpContext.Abort();
+                    try
+                    {
+                        await httpContext.Response.WriteAsync($"hello, world");
+                        tcs.SetResult(null);
+                    }
+                    catch (Exception ex)
+                    {
+                        tcs.SetException(ex);
+                    }
+                }));
+
+            using (var host = hostBuilder.Build())
+            {
+                host.Start();
+
+                using (var socket = await HttpClientSlim.GetSocket(new Uri($"https://127.0.0.1:{host.GetPort()}/")))
+                using (var stream = new NetworkStream(socket, ownsSocket: false))
+                using (var sslStream = new SslStream(stream, true, (sender, certificate, chain, errors) => true))
+                {
+                    await sslStream.AuthenticateAsClientAsync("127.0.0.1", clientCertificates: null,
+                        enabledSslProtocols: SslProtocols.Tls11 | SslProtocols.Tls12,
+                        checkCertificateRevocation: false);
+
+                    var request = Encoding.ASCII.GetBytes("GET / HTTP/1.1\r\n\r\n");
+                    await sslStream.WriteAsync(request, 0, request.Length);
+                    await sslStream.ReadAsync(new byte[32], 0, 32);
+                }
+            }
+
+            await tcs.Task.TimeoutAfter(TimeSpan.FromSeconds(10));
+        }
+
         private class HandshakeErrorLoggerFactory : ILoggerFactory
         {
             public HttpsConnectionFilterLogger FilterLogger { get; } = new HttpsConnectionFilterLogger();
diff --git a/test/Microsoft.AspNetCore.Server.KestrelTests/FrameTests.cs b/test/Microsoft.AspNetCore.Server.KestrelTests/FrameTests.cs
index b411dc6b8f..be5c3e9348 100644
--- a/test/Microsoft.AspNetCore.Server.KestrelTests/FrameTests.cs
+++ b/test/Microsoft.AspNetCore.Server.KestrelTests/FrameTests.cs
@@ -6,6 +6,8 @@ using System.IO;
 using System.Text;
 using System.Threading;
 using System.Threading.Tasks;
+using Microsoft.AspNetCore.Hosting.Server;
+using Microsoft.AspNetCore.Http;
 using Microsoft.AspNetCore.Http.Features;
 using Microsoft.AspNetCore.Server.Kestrel;
 using Microsoft.AspNetCore.Server.Kestrel.Internal;
@@ -1290,7 +1292,7 @@ namespace Microsoft.AspNetCore.Server.KestrelTests
                 var expectedKeepAliveTimeout = (long)serviceContext.ServerOptions.Limits.KeepAliveTimeout.TotalMilliseconds;
                 connectionControl.Verify(cc => cc.SetTimeout(expectedKeepAliveTimeout, TimeoutAction.CloseConnection));
 
-                frame.Stop();
+                frame.StopAsync();
                 socketInput.IncomingFin();
 
                 requestProcessingTask.Wait();
@@ -1464,5 +1466,43 @@ namespace Microsoft.AspNetCore.Server.KestrelTests
             // Assert
             Assert.Throws<InvalidOperationException>(() => frame.Flush());
         }
+
+        [Fact]
+        public async Task RequestProcessingTaskIsUnwrapped()
+        {
+            var trace = new KestrelTrace(new TestKestrelTrace());
+            var ltp = new LoggingThreadPool(trace);
+            using (var pool = new MemoryPool())
+            using (var socketInput = new SocketInput(pool, ltp))
+            {
+                var serviceContext = new ServiceContext
+                {
+                    DateHeaderValueManager = new DateHeaderValueManager(),
+                    ServerOptions = new KestrelServerOptions(),
+                    Log = trace
+                };
+                var listenerContext = new ListenerContext(serviceContext)
+                {
+                    ServerAddress = ServerAddress.FromUrl("http://localhost:5000")
+                };
+                var connectionContext = new ConnectionContext(listenerContext)
+                {
+                    ConnectionControl = Mock.Of<IConnectionControl>(),
+                    SocketInput = socketInput
+                };
+
+                var frame = new Frame<HttpContext>(application: null, context: connectionContext);
+                frame.Start();
+
+                var data = Encoding.ASCII.GetBytes("GET / HTTP/1.1\r\n\r\n");
+                socketInput.IncomingData(data, 0, data.Length);
+
+                var requestProcessingTask = frame.StopAsync();
+                Assert.IsNotType(typeof(Task<Task>), requestProcessingTask);
+
+                await requestProcessingTask.TimeoutAfter(TimeSpan.FromSeconds(10));
+                socketInput.IncomingFin();
+            }
+        }
     }
 }