diff --git a/homeassistant/components/history/websocket_api.py b/homeassistant/components/history/websocket_api.py
index 1f1c5064c5a..6eb1fec3416 100644
--- a/homeassistant/components/history/websocket_api.py
+++ b/homeassistant/components/history/websocket_api.py
@@ -36,6 +36,7 @@ from homeassistant.helpers.event import (
     async_track_state_change_event,
 )
 from homeassistant.helpers.json import json_bytes
+from homeassistant.util.async_ import create_eager_task
 import homeassistant.util.dt as dt_util
 
 from .const import EVENT_COALESCE_TIME, MAX_PENDING_HISTORY_STATES
@@ -536,7 +537,7 @@ async def ws_stream(
         # Unsubscribe happened while sending historical states
         return
 
-    live_stream.task = asyncio.create_task(
+    live_stream.task = create_eager_task(
         _async_events_consumer(
             subscriptions_setup_complete_time,
             connection,
@@ -546,7 +547,7 @@ async def ws_stream(
         )
     )
 
-    live_stream.wait_sync_task = asyncio.create_task(
+    live_stream.wait_sync_task = create_eager_task(
         get_instance(hass).async_block_till_done()
     )
     await live_stream.wait_sync_task
diff --git a/homeassistant/components/logbook/websocket_api.py b/homeassistant/components/logbook/websocket_api.py
index 4e4732c0d0e..6d976a50240 100644
--- a/homeassistant/components/logbook/websocket_api.py
+++ b/homeassistant/components/logbook/websocket_api.py
@@ -18,6 +18,7 @@ from homeassistant.components.websocket_api.connection import ActiveConnection
 from homeassistant.core import CALLBACK_TYPE, Event, HomeAssistant, callback
 from homeassistant.helpers.event import async_track_point_in_utc_time
 from homeassistant.helpers.json import json_bytes
+from homeassistant.util.async_ import create_eager_task
 import homeassistant.util.dt as dt_util
 
 from .const import DOMAIN
@@ -395,7 +396,7 @@ async def ws_event_stream(
         # Unsubscribe happened while sending historical events
         return
 
-    live_stream.task = asyncio.create_task(
+    live_stream.task = create_eager_task(
         _async_events_consumer(
             subscriptions_setup_complete_time,
             connection,
@@ -405,7 +406,7 @@ async def ws_event_stream(
         )
     )
 
-    live_stream.wait_sync_task = asyncio.create_task(
+    live_stream.wait_sync_task = create_eager_task(
         get_instance(hass).async_block_till_done()
     )
     await live_stream.wait_sync_task