diff --git a/vllm/entrypoints/openai/api_server.py b/vllm/entrypoints/openai/api_server.py
index 2a61259896a37..1e7d9eb83b9af 100644
--- a/vllm/entrypoints/openai/api_server.py
+++ b/vllm/entrypoints/openai/api_server.py
@@ -1098,9 +1098,10 @@ async def run_server(args, **uvicorn_kwargs) -> None:
         )
 
     # NB: Await server shutdown only after the backend context is exited
-    await shutdown_task
-
-    sock.close()
+    try:
+        await shutdown_task
+    finally:
+        sock.close()
 
 
 if __name__ == "__main__":