diff --git a/tornado/gen.py b/tornado/gen.py
index 4819b85715..dab4fd09db 100644
--- a/tornado/gen.py
+++ b/tornado/gen.py
@@ -840,13 +840,17 @@ def handle_exception(
             return False
 
 
-# Convert Awaitables into Futures.
-try:
-    _wrap_awaitable = asyncio.ensure_future
-except AttributeError:
-    # asyncio.ensure_future was introduced in Python 3.4.4, but
-    # Debian jessie still ships with 3.4.2 so try the old name.
-    _wrap_awaitable = getattr(asyncio, "async")
+def _wrap_awaitable(awaitable: Awaitable) -> Future:
+    # Convert Awaitables into Futures.
+    # Note that we use ensure_future, which handles both awaitables
+    # and coroutines, rather than create_task, which only accepts
+    # coroutines. (ensure_future calls create_task if given a coroutine)
+    fut = asyncio.ensure_future(awaitable)
+    # See comments on IOLoop._pending_tasks.
+    loop = IOLoop.current()
+    loop._register_task(fut)
+    fut.add_done_callback(lambda f: loop._unregister_task(f))
+    return fut
 
 
 def convert_yielded(yielded: _Yieldable) -> Future:
diff --git a/tornado/ioloop.py b/tornado/ioloop.py
index bcdcca097b..1958df0cc7 100644
--- a/tornado/ioloop.py
+++ b/tornado/ioloop.py
@@ -50,7 +50,7 @@
 from typing import Union, Any, Type, Optional, Callable, TypeVar, Tuple, Awaitable
 
 if typing.TYPE_CHECKING:
-    from typing import Dict, List  # noqa: F401
+    from typing import Dict, List, Set  # noqa: F401
 
     from typing_extensions import Protocol
 else:
@@ -159,6 +159,18 @@ async def main():
     # In Python 3, _ioloop_for_asyncio maps from asyncio loops to IOLoops.
     _ioloop_for_asyncio = dict()  # type: Dict[asyncio.AbstractEventLoop, IOLoop]
 
+    # Maintain a set of all pending tasks to follow the warning in the docs
+    # of asyncio.create_tasks:
+    # https://docs.python.org/3.11/library/asyncio-task.html#asyncio.create_task
+    # This ensures that all pending tasks have a strong reference so they
+    # will not be garbage collected before they are finished.
+    # (Thus avoiding "task was destroyed but it is pending" warnings)
+    # An analogous change has been proposed in cpython for 3.13:
+    # https://github.com/python/cpython/issues/91887
+    # If that change is accepted, this can eventually be removed.
+    # If it is not, we will consider the rationale and may remove this.
+    _pending_tasks = set()  # type: Set[Future]
+
     @classmethod
     def configure(
         cls, impl: "Union[None, str, Type[Configurable]]", **kwargs: Any
@@ -803,6 +815,12 @@ def close_fd(self, fd: Union[int, _Selectable]) -> None:
         except OSError:
             pass
 
+    def _register_task(self, f: Future) -> None:
+        self._pending_tasks.add(f)
+
+    def _unregister_task(self, f: Future) -> None:
+        self._pending_tasks.discard(f)
+
 
 class _Timeout(object):
     """An IOLoop timeout, a UNIX timestamp and a callback"""