diff --git a/src/libraries/Common/tests/System/Net/Http/HttpClientHandlerTest.Asynchrony.cs b/src/libraries/Common/tests/System/Net/Http/HttpClientHandlerTest.Asynchrony.cs
index 8762b4dbfa9348..276ca98ce001d5 100644
--- a/src/libraries/Common/tests/System/Net/Http/HttpClientHandlerTest.Asynchrony.cs
+++ b/src/libraries/Common/tests/System/Net/Http/HttpClientHandlerTest.Asynchrony.cs
@@ -31,6 +31,11 @@ public async Task ResponseHeadersRead_SynchronizationContextNotUsedByHandler(boo
                 return;
             }
 
+            if (UseVersion.Major != 1)
+            {
+                return;
+            }
+
             await Task.Run(async delegate // escape xunit's sync ctx
             {
                 await LoopbackServer.CreateClientAndServerAsync(uri =>
diff --git a/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http2Connection.cs b/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http2Connection.cs
index 862ac35498719a..ae9dfb1024b68b 100644
--- a/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http2Connection.cs
+++ b/src/libraries/System.Net.Http/src/System/Net/Http/SocketsHttpHandler/Http2Connection.cs
@@ -225,7 +225,12 @@ public async ValueTask SetupAsync(CancellationToken cancellationToken)
 
                 // Processing the incoming frames before sending the client preface and SETTINGS is necessary when using a NamedPipe as a transport.
                 // If the preface and SETTINGS coming from the server are not read first the below WriteAsync and the ProcessIncomingFramesAsync fall into a deadlock.
-                _ = ProcessIncomingFramesAsync();
+                // Avoid capturing the initial request's ExecutionContext for the entire lifetime of the new connection.
+                using (ExecutionContext.SuppressFlow())
+                {
+                    _ = ProcessIncomingFramesAsync();
+                }
+
                 await _stream.WriteAsync(_outgoingBuffer.ActiveMemory, cancellationToken).ConfigureAwait(false);
                 _rttEstimator.OnInitialSettingsSent();
                 _outgoingBuffer.ClearAndReturnBuffer();
@@ -249,7 +254,11 @@ public async ValueTask SetupAsync(CancellationToken cancellationToken)
                 throw new IOException(SR.net_http_http2_connection_not_established, e);
             }
 
-            _ = ProcessOutgoingFramesAsync();
+            // Avoid capturing the initial request's ExecutionContext for the entire lifetime of the new connection.
+            using (ExecutionContext.SuppressFlow())
+            {
+                _ = ProcessOutgoingFramesAsync();
+            }
         }
 
         private void Shutdown()
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 379c97d5c70754..fbf3e40d5cb216 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
@@ -95,11 +95,15 @@ public void InitQuicConnection(QuicConnection connection, Activity? connectionSe
 
             _connection = connection;
 
-            // Errors are observed via Abort().
-            _sendSettingsTask = SendSettingsAsync();
+            // Avoid capturing the initial request's ExecutionContext for the entire lifetime of the new connection.
+            using (ExecutionContext.SuppressFlow())
+            {
+                // Errors are observed via Abort().
+                _sendSettingsTask = SendSettingsAsync();
 
-            // This process is cleaned up when _connection is disposed, and errors are observed via Abort().
-            _ = AcceptStreamsAsync();
+                // This process is cleaned up when _connection is disposed, and errors are observed via Abort().
+                _ = AcceptStreamsAsync();
+            }
         }
 
         /// <summary>
diff --git a/src/libraries/System.Net.Http/tests/FunctionalTests/SocketsHttpHandlerTest.cs b/src/libraries/System.Net.Http/tests/FunctionalTests/SocketsHttpHandlerTest.cs
index 7a82f848e78a95..70c4c72760a59b 100644
--- a/src/libraries/System.Net.Http/tests/FunctionalTests/SocketsHttpHandlerTest.cs
+++ b/src/libraries/System.Net.Http/tests/FunctionalTests/SocketsHttpHandlerTest.cs
@@ -28,10 +28,9 @@ namespace System.Net.Http.Functional.Tests
 {
     using Configuration = System.Net.Test.Common.Configuration;
 
-    [ConditionalClass(typeof(PlatformDetection), nameof(PlatformDetection.IsNotBrowser))]
-    public sealed class SocketsHttpHandler_HttpClientHandler_Asynchrony_Test : HttpClientHandler_Asynchrony_Test
+    public sealed class SocketsHttpHandler_HttpClientHandler_Asynchrony_Test_Http11 : SocketsHttpHandler_HttpClientHandler_Asynchrony_Test
     {
-        public SocketsHttpHandler_HttpClientHandler_Asynchrony_Test(ITestOutputHelper output) : base(output) { }
+        public SocketsHttpHandler_HttpClientHandler_Asynchrony_Test_Http11(ITestOutputHelper output) : base(output) { }
 
         [OuterLoop("Relies on finalization")]
         [Fact]
@@ -98,6 +97,25 @@ static async Task MakeARequestWithoutDisposingTheHandlerAsync()
                 requestCompleted.SetResult();
             }
         }
+    }
+
+    public sealed class SocketsHttpHandler_HttpClientHandler_Asynchrony_Test_Http2 : SocketsHttpHandler_HttpClientHandler_Asynchrony_Test
+    {
+        public SocketsHttpHandler_HttpClientHandler_Asynchrony_Test_Http2(ITestOutputHelper output) : base(output) { }
+        protected override Version UseVersion => HttpVersion.Version20;
+    }
+
+    [ConditionalClass(typeof(HttpClientHandlerTestBase), nameof(IsQuicSupported))]
+    public sealed class SocketsHttpHandler_HttpClientHandler_Asynchrony_Test_Http3 : SocketsHttpHandler_HttpClientHandler_Asynchrony_Test
+    {
+        public SocketsHttpHandler_HttpClientHandler_Asynchrony_Test_Http3(ITestOutputHelper output) : base(output) { }
+        protected override Version UseVersion => HttpVersion.Version30;
+    }
+
+    [ConditionalClass(typeof(PlatformDetection), nameof(PlatformDetection.IsNotBrowser))]
+    public abstract class SocketsHttpHandler_HttpClientHandler_Asynchrony_Test : HttpClientHandler_Asynchrony_Test
+    {
+        public SocketsHttpHandler_HttpClientHandler_Asynchrony_Test(ITestOutputHelper output) : base(output) { }
 
         [Fact]
         public async Task ReadAheadTaskOnConnectionReuse_ExceptionsAreObserved()
@@ -191,7 +209,7 @@ await LoopbackServerFactory.CreateClientAndServerAsync(
         public async Task ExecutionContext_HttpConnectionLifetimeDoesntKeepContextAlive()
         {
             var clientCompleted = new TaskCompletionSource(TaskCreationOptions.RunContinuationsAsynchronously);
-            await LoopbackServer.CreateClientAndServerAsync(async uri =>
+            await LoopbackServerFactory.CreateClientAndServerAsync(async uri =>
             {
                 try
                 {
@@ -217,7 +235,9 @@ await LoopbackServer.CreateClientAndServerAsync(async uri =>
             {
                 await server.AcceptConnectionAsync(async connection =>
                 {
-                    await connection.ReadRequestHeaderAndSendResponseAsync();
+                    await connection.ReadRequestDataAsync();
+                    await connection.SendResponseAsync();
+
                     await clientCompleted.Task;
                 });
             });
@@ -240,7 +260,7 @@ private static (Task completedOnFinalized, Task getRequest) MakeHttpRequestWithT
             return (tcs.Task, t);
         }
 
-        private sealed class SetOnFinalized
+        protected sealed class SetOnFinalized
         {
             public readonly TaskCompletionSource CompletedWhenFinalized = new(TaskCreationOptions.RunContinuationsAsynchronously);