diff --git a/playwright/_impl/_connection.py b/playwright/_impl/_connection.py
index 3c0cd6da4..578f77ad6 100644
--- a/playwright/_impl/_connection.py
+++ b/playwright/_impl/_connection.py
@@ -168,8 +168,9 @@ def stop_sync(self) -> None:
         self._transport.stop()
         self._dispatcher_fiber.switch()
 
-    def stop_async(self) -> None:
+    async def stop_async(self) -> None:
         self._transport.stop()
+        await self._transport.wait_until_stopped()
 
     async def wait_for_object_with_known_name(self, guid: str) -> Any:
         if guid in self._objects:
diff --git a/playwright/_impl/_transport.py b/playwright/_impl/_transport.py
index 8e07ad1e7..331b1a523 100644
--- a/playwright/_impl/_transport.py
+++ b/playwright/_impl/_transport.py
@@ -46,8 +46,12 @@ def stop(self) -> None:
         self._stopped = True
         self._output.close()
 
+    async def wait_until_stopped(self) -> None:
+        await self._stopped_future
+
     async def run(self) -> None:
         self._loop = asyncio.get_running_loop()
+        self._stopped_future: asyncio.Future = asyncio.Future()
 
         driver_env = os.environ.copy()
         # VSCode's JavaScript Debug Terminal provides it but driver/pkg does not support it
@@ -87,6 +91,7 @@ async def run(self) -> None:
             except asyncio.IncompleteReadError:
                 break
             await asyncio.sleep(0)
+        self._stopped_future.set_result(None)
 
     def send(self, message: Dict) -> None:
         msg = json.dumps(message)
diff --git a/playwright/async_api/_context_manager.py b/playwright/async_api/_context_manager.py
index 16821e762..2b64e20ae 100644
--- a/playwright/async_api/_context_manager.py
+++ b/playwright/async_api/_context_manager.py
@@ -42,4 +42,4 @@ async def start(self) -> AsyncPlaywright:
         return await self.__aenter__()
 
     async def __aexit__(self, *args: Any) -> None:
-        self._connection.stop_async()
+        await self._connection.stop_async()