diff --git a/redis/asyncio/client.py b/redis/asyncio/client.py
index e4d2e776bc..acc89941f2 100644
--- a/redis/asyncio/client.py
+++ b/redis/asyncio/client.py
@@ -546,6 +546,7 @@ def __del__(
                 _grl().call_exception_handler(context)
             except RuntimeError:
                 pass
+            self.connection._close()
 
     async def aclose(self, close_connection_pool: Optional[bool] = None) -> None:
         """
diff --git a/redis/asyncio/connection.py b/redis/asyncio/connection.py
index 1ef9960ff3..7b0443454b 100644
--- a/redis/asyncio/connection.py
+++ b/redis/asyncio/connection.py
@@ -5,6 +5,7 @@
 import socket
 import ssl
 import sys
+import warnings
 import weakref
 from abc import abstractmethod
 from itertools import chain
@@ -204,6 +205,24 @@ def __init__(
                 raise ConnectionError("protocol must be either 2 or 3")
             self.protocol = protocol
 
+    def __del__(self, _warnings: Any = warnings):
+        # For some reason, the individual streams don't get properly garbage
+        # collected and therefore produce no resource warnings.  We add one
+        # here, in the same style as those from the stdlib.
+        if getattr(self, "_writer", None):
+            _warnings.warn(
+                f"unclosed Connection {self!r}", ResourceWarning, source=self
+            )
+            self._close()
+
+    def _close(self):
+        """
+        Internal method to silently close the connection without waiting
+        """
+        if self._writer:
+            self._writer.close()
+            self._writer = self._reader = None
+
     def __repr__(self):
         repr_args = ",".join((f"{k}={v}" for k, v in self.repr_pieces()))
         return f"{self.__class__.__name__}<{repr_args}>"
@@ -1017,7 +1036,7 @@ def __repr__(self):
 
     def reset(self):
         self._available_connections = []
-        self._in_use_connections = set()
+        self._in_use_connections = weakref.WeakSet()
 
     def can_get_connection(self) -> bool:
         """Return True if a connection can be retrieved from the pool."""
diff --git a/tests/test_asyncio/test_connection.py b/tests/test_asyncio/test_connection.py
index 28e6b0d9c3..474a906091 100644
--- a/tests/test_asyncio/test_connection.py
+++ b/tests/test_asyncio/test_connection.py
@@ -316,7 +316,8 @@ async def mock_aclose(self):
     url: str = request.config.getoption("--redis-url")
     r1 = await Redis.from_url(url)
     with patch.object(r1, "aclose", mock_aclose):
-        await r1.close()
+        with pytest.deprecated_call():
+            await r1.close()
         assert calls == 1
 
     with pytest.deprecated_call():
@@ -436,3 +437,52 @@ async def mock_disconnect(_):
 
     assert called == 0
     await pool.disconnect()
+
+
+async def test_client_garbage_collection(request):
+    """
+    Test that a Redis client will call _close() on any
+    connection that it holds at time of destruction
+    """
+
+    url: str = request.config.getoption("--redis-url")
+    pool = ConnectionPool.from_url(url)
+
+    # create a client with a connection from the pool
+    client = Redis(connection_pool=pool, single_connection_client=True)
+    await client.initialize()
+    with mock.patch.object(client, "connection") as a:
+        # we cannot, in unittests, or from asyncio, reliably trigger garbage collection
+        # so we must just invoke the handler
+        with pytest.warns(ResourceWarning):
+            client.__del__()
+            assert a._close.called
+
+    await client.aclose()
+    await pool.aclose()
+
+
+async def test_connection_garbage_collection(request):
+    """
+    Test that a Connection object will call close() on the
+    stream that it holds.
+    """
+
+    url: str = request.config.getoption("--redis-url")
+    pool = ConnectionPool.from_url(url)
+
+    # create a client with a connection from the pool
+    client = Redis(connection_pool=pool, single_connection_client=True)
+    await client.initialize()
+    conn = client.connection
+
+    with mock.patch.object(conn, "_reader"):
+        with mock.patch.object(conn, "_writer") as a:
+            # we cannot, in unittests, or from asyncio, reliably trigger
+            # garbage collection so we must just invoke the handler
+            with pytest.warns(ResourceWarning):
+                conn.__del__()
+                assert a.close.called
+
+    await client.aclose()
+    await pool.aclose()