diff --git a/src/Microsoft.AspNetCore.Sockets.Client/Connection.cs b/src/Microsoft.AspNetCore.Sockets.Client/Connection.cs
index 2fa57d2ac2..3312afc0e6 100644
--- a/src/Microsoft.AspNetCore.Sockets.Client/Connection.cs
+++ b/src/Microsoft.AspNetCore.Sockets.Client/Connection.cs
@@ -104,6 +104,7 @@ namespace Microsoft.AspNetCore.Sockets.Client
         {
             Output.TryComplete();
             await _transport.StopAsync();
+            await DrainMessages();
         }
 
         public void Dispose()
@@ -112,6 +113,17 @@ namespace Microsoft.AspNetCore.Sockets.Client
             _transport.Dispose();
         }
 
+        private async Task DrainMessages()
+        {
+            while (await Input.WaitToReadAsync())
+            {
+                if (Input.TryRead(out Message message))
+                {
+                    message.Dispose();
+                }
+            }
+        }
+
         public static Task<Connection> ConnectAsync(Uri url, ITransport transport) => ConnectAsync(url, transport, null, null);
         public static Task<Connection> ConnectAsync(Uri url, ITransport transport, ILoggerFactory loggerFactory) => ConnectAsync(url, transport, null, loggerFactory);
         public static Task<Connection> ConnectAsync(Uri url, ITransport transport, HttpClient httpClient) => ConnectAsync(url, transport, httpClient, null);