diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index f69abc80a3c013..7260f59868e63a 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -1120,6 +1120,8 @@ class Http2Session extends EventEmitter {
     if (!socket._handle || !socket._handle.isStreamBase) {
       socket = new JSStreamSocket(socket);
     }
+    socket.on('error', socketOnError);
+    socket.on('close', socketOnClose);
 
     // No validation is performed on the input parameters because this
     // constructor is not exported directly for users.
@@ -2887,9 +2889,6 @@ function connectionListener(socket) {
     return;
   }
 
-  socket.on('error', socketOnError);
-  socket.on('close', socketOnClose);
-
   // Set up the Session
   const session = new ServerHttp2Session(options, socket, this);
 
@@ -3100,12 +3099,6 @@ function connect(authority, options, listener) {
 
   const session = new ClientHttp2Session(options, socket);
 
-  // ClientHttp2Session may create a new socket object
-  // when socket is a JSSocket (socket != kSocket)
-  // https://github.com/nodejs/node/issues/35695
-  session[kSocket].on('error', socketOnError);
-  session[kSocket].on('close', socketOnClose);
-
   session[kAuthority] = `${options.servername || host}:${port}`;
   session[kProtocol] = protocol;
 
diff --git a/test/parallel/test-http2-client-jsstream-destroy.js b/test/parallel/test-http2-client-jsstream-destroy.js
index f2f0669170c4bc..f881eac47aa809 100644
--- a/test/parallel/test-http2-client-jsstream-destroy.js
+++ b/test/parallel/test-http2-client-jsstream-destroy.js
@@ -46,9 +46,9 @@ server.listen(0, common.mustCall(function() {
     });
     const req = client.request();
 
-    setTimeout(() => socket.destroy(), 200);
-    setTimeout(() => client.close(), 400);
-    setTimeout(() => server.close(), 600);
+    setTimeout(() => socket.destroy(), common.platformTimeout(100));
+    setTimeout(() => client.close(), common.platformTimeout(200));
+    setTimeout(() => server.close(), common.platformTimeout(300));
 
     req.on('close', common.mustCall(() => { }));
   });