diff --git a/tests/common.py b/tests/common.py
index 3ed0f9e2008..88450d34564 100644
--- a/tests/common.py
+++ b/tests/common.py
@@ -353,13 +353,13 @@ async def async_test_home_assistant(
 
     hass.set_state(CoreState.running)
 
-    @callback
-    def clear_instance(event):
+    async def clear_instance(event):
         """Clear global instance."""
+        await asyncio.sleep(0)  # Give aiohttp one loop iteration to close
         INSTANCES.remove(hass)
 
     hass.bus.async_listen_once(
-        EVENT_HOMEASSISTANT_CLOSE, clear_instance, run_immediately=False
+        EVENT_HOMEASSISTANT_CLOSE, clear_instance, run_immediately=True
     )
 
     yield hass
diff --git a/tests/components/automation/test_init.py b/tests/components/automation/test_init.py
index ba02e61f0a7..439ca76d545 100644
--- a/tests/components/automation/test_init.py
+++ b/tests/components/automation/test_init.py
@@ -2506,6 +2506,7 @@ async def test_recursive_automation_starting_script(
         async def async_automation_triggered(event):
             """Listen to automation_triggered event from the automation integration."""
             automation_triggered.append(event)
+            await asyncio.sleep(0)  # Yield to allow other tasks to run
             hass.states.async_set("sensor.test", str(len(automation_triggered)))
 
         hass.services.async_register("test", "script_done", async_service_handler)
@@ -2513,7 +2514,7 @@ async def test_recursive_automation_starting_script(
             "test", "automation_started", async_service_handler
         )
         hass.bus.async_listen(
-            "automation_triggered", async_automation_triggered, run_immediately=False
+            "automation_triggered", async_automation_triggered, run_immediately=True
         )
 
         hass.bus.async_fire("trigger_automation")