diff --git a/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http3Connection.cs b/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http3Connection.cs
index 75b9d9b1f8a964..b76c0b79ec0665 100644
--- a/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http3Connection.cs
+++ b/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http3Connection.cs
@@ -28,6 +28,8 @@ internal sealed class Http3Connection : HttpConnectionBase
         // Keep a collection of requests around so we can process GOAWAY.
         private readonly Dictionary<QuicStream, Http3RequestStream> _activeRequests = new Dictionary<QuicStream, Http3RequestStream>();
 
+        internal readonly List<Task> _streamDisposals = [];
+
         // Set when GOAWAY is being processed, when aborting, or when disposing.
         private long _firstRejectedStreamId = -1;
 
@@ -126,6 +128,10 @@ private void CheckForShutdown()
 
             if (_connection != null)
             {
+                // Make sure we've disposed every stream before closing the connection.
+
+                Task.WhenAll(_streamDisposals).GetAwaiter().GetResult();
+
                 // Close the QuicConnection in the background.
 
                 _connectionClosedTask ??= _connection.CloseAsync((long)Http3ErrorCode.NoError).AsTask();
@@ -363,6 +369,14 @@ public void RemoveStream(QuicStream stream)
             }
         }
 
+        public void QueueStreamForDisposal(QuicStream stream)
+        {
+            lock (SyncObj)
+            {
+                _streamDisposals.Add(stream.DisposeAsync().AsTask());
+            }
+        }
+
         public override long GetIdleTicks(long nowTicks) => throw new NotImplementedException("We aren't scavenging HTTP3 connections yet");
 
         public override void Trace(string message, [CallerMemberName] string? memberName = null) =>
diff --git a/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http3RequestStream.cs b/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http3RequestStream.cs
index ef2532b2b22d08..67d2487b9c0edd 100644
--- a/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http3RequestStream.cs
+++ b/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http3RequestStream.cs
@@ -88,7 +88,7 @@ public void Dispose()
             {
                 _disposed = true;
                 AbortStream();
-                _stream.Dispose();
+                _connection.QueueStreamForDisposal(_stream);
                 DisposeSyncHelper();
             }
         }