diff --git a/distributed/batched.py b/distributed/batched.py
index aa001322b25..9050516783d 100644
--- a/distributed/batched.py
+++ b/distributed/batched.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import contextlib
 import logging
 from collections import deque
 from typing import Any
@@ -94,9 +95,24 @@ def _background_send(self):
             self.batch_count += 1
             self.next_deadline = time() + self.interval
             try:
-                nbytes = yield self.comm.write(
-                    payload, serializers=self.serializers, on_error="raise"
-                )
+                # NOTE: Since `BatchedSend` doesn't have a handle on the running
+                # `_background_send` coroutine, the only thing with a reference to this
+                # coroutine is the event loop itself. If the event loop stops while
+                # we're waiting on a `write`, the `_background_send` coroutine object
+                # may be garbage collected. If that happens, the `yield coro` will raise
+                # `GeneratorExit`. But because this is an old-school `gen.coroutine`,
+                # and we're using `yield` and not `await`, the `write` coroutine object
+                # will not actually have been awaited, and it will remain sitting around
+                # for someone to retrieve it. At interpreter exit, this will warn
+                # sommething like `RuntimeWarning: coroutine 'TCP.write' was never
+                # awaited`. By using the `closing` contextmanager, the `write` coroutine
+                # object is always cleaned up, even if `yield` raises `GeneratorExit`.
+                with contextlib.closing(
+                    self.comm.write(
+                        payload, serializers=self.serializers, on_error="raise"
+                    )
+                ) as coro:
+                    nbytes = yield coro
                 if nbytes < 1e6:
                     self.recent_message_log.append(payload)
                 else:
@@ -160,9 +176,13 @@ def close(self, timeout=None):
             try:
                 if self.buffer:
                     self.buffer, payload = [], self.buffer
-                    yield self.comm.write(
-                        payload, serializers=self.serializers, on_error="raise"
-                    )
+                    # See note in `_background_send` for explanation of `closing`.
+                    with contextlib.closing(
+                        self.comm.write(
+                            payload, serializers=self.serializers, on_error="raise"
+                        )
+                    ) as coro:
+                        yield coro
             except CommClosedError:
                 pass
             yield self.comm.close()