diff --git a/fastapi/routing.py b/fastapi/routing.py
index a52271690f..e2c83aa7b3 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -30,6 +30,7 @@ from typing import (
 
 import anyio
 from annotated_doc import Doc
+from anyio.abc import ObjectReceiveStream
 from fastapi import params
 from fastapi._compat import (
     ModelField,
@@ -526,7 +527,10 @@ def get_request_handler(
                 else:
                     sse_aiter = iterate_in_threadpool(gen)
 
-                async def _async_stream_sse() -> AsyncIterator[bytes]:
+                @asynccontextmanager
+                async def _sse_producer_cm() -> AsyncIterator[
+                    ObjectReceiveStream[bytes]
+                ]:
                     # Use a memory stream to decouple generator iteration
                     # from the keepalive timer. A producer task pulls items
                     # from the generator independently, so
@@ -534,6 +538,13 @@ def get_request_handler(
                     # `__anext__` directly - avoiding CancelledError that
                     # would finalize the generator and also working for sync
                     # generators running in a thread pool.
+                    #
+                    # This context manager is entered on the request-scoped
+                    # AsyncExitStack so its __aexit__ (which cancels the
+                    # task group) is called by the exit stack after the
+                    # streaming response completes — not by async generator
+                    # finalization via GeneratorExit.
+                    # Ref: https://peps.python.org/pep-0789/
                     send_stream, receive_stream = anyio.create_memory_object_stream[
                         bytes
                     ](max_buffer_size=1)
@@ -543,25 +554,54 @@ def get_request_handler(
                             async for raw_item in sse_aiter:
                                 await send_stream.send(_serialize_sse_item(raw_item))
 
-                    async with anyio.create_task_group() as tg:
-                        tg.start_soon(_producer)
-                        async with receive_stream:
+                    send_keepalive, receive_keepalive = (
+                        anyio.create_memory_object_stream[bytes](max_buffer_size=1)
+                    )
+
+                    async def _keepalive_inserter() -> None:
+                        """Read from the producer and forward to the output,
+                        inserting keepalive comments on timeout."""
+                        async with send_keepalive, receive_stream:
                             try:
                                 while True:
                                     try:
                                         with anyio.fail_after(_PING_INTERVAL):
                                             data = await receive_stream.receive()
-                                        yield data
-                                        # To allow for cancellation to trigger
-                                        # Ref: https://github.com/fastapi/fastapi/issues/14680
-                                        await anyio.sleep(0)
+                                        await send_keepalive.send(data)
                                     except TimeoutError:
-                                        yield KEEPALIVE_COMMENT
+                                        await send_keepalive.send(KEEPALIVE_COMMENT)
                             except anyio.EndOfStream:
                                 pass
 
+                    async with anyio.create_task_group() as tg:
+                        tg.start_soon(_producer)
+                        tg.start_soon(_keepalive_inserter)
+                        yield receive_keepalive
+                        tg.cancel_scope.cancel()
+
+                # Enter the SSE context manager on the request-scoped
+                # exit stack. The stack outlives the streaming response,
+                # so __aexit__ runs via proper structured teardown, not
+                # via GeneratorExit thrown into an async generator.
+                sse_receive_stream = await async_exit_stack.enter_async_context(
+                    _sse_producer_cm()
+                )
+                # Ensure the receive stream is closed when the exit stack
+                # unwinds, preventing ResourceWarning from __del__.
+                async_exit_stack.push_async_callback(sse_receive_stream.aclose)
+
+                async def _sse_with_checkpoints(
+                    stream: ObjectReceiveStream[bytes],
+                ) -> AsyncIterator[bytes]:
+                    async for data in stream:
+                        yield data
+                        # Guarantee a checkpoint so cancellation can be
+                        # delivered even when the producer is faster than
+                        # the consumer and receive() never suspends.
+                        await anyio.sleep(0)
+
                 sse_stream_content: AsyncIterator[bytes] | Iterator[bytes] = (
-                    _async_stream_sse()
+                    _sse_with_checkpoints(sse_receive_stream)
                 )
 
                 response = StreamingResponse(