diff --git a/homeassistant/helpers/script.py b/homeassistant/helpers/script.py
index c724b9e890d..107cd9e2106 100644
--- a/homeassistant/helpers/script.py
+++ b/homeassistant/helpers/script.py
@@ -393,58 +393,85 @@ class _ScriptRun(_ScriptRunBase):
         except KeyError:
             delay = None
         done = asyncio.Event()
+        tasks = [
+            self._hass.async_create_task(flag.wait()) for flag in (self._stop, done)
+        ]
         try:
             async with timeout(delay):
-                _, pending = await asyncio.wait(
-                    {self._stop.wait(), done.wait()},
-                    return_when=asyncio.FIRST_COMPLETED,
-                )
-            for pending_task in pending:
-                pending_task.cancel()
+                await asyncio.wait(tasks, return_when=asyncio.FIRST_COMPLETED)
         except asyncio.TimeoutError:
             if not self._action.get(CONF_CONTINUE_ON_TIMEOUT, True):
                 self._log(_TIMEOUT_MSG)
                 raise _StopScript
         finally:
+            for task in tasks:
+                task.cancel()
             unsub()
 
     async def _async_call_service_step(self):
         """Call the service specified in the action."""
         domain, service, service_data = self._prep_call_service_step()
 
+        running_script = (
+            domain == "automation"
+            and service == "trigger"
+            or domain == "python_script"
+            or domain == "script"
+            and service != SERVICE_TURN_OFF
+        )
         # If this might start a script then disable the call timeout.
         # Otherwise use the normal service call limit.
-        if domain == "script" and service != SERVICE_TURN_OFF:
+        if running_script:
             limit = None
         else:
             limit = SERVICE_CALL_LIMIT
 
-        coro = self._hass.services.async_call(
-            domain,
-            service,
-            service_data,
-            blocking=True,
-            context=self._context,
-            limit=limit,
+        service_task = self._hass.async_create_task(
+            self._hass.services.async_call(
+                domain,
+                service,
+                service_data,
+                blocking=True,
+                context=self._context,
+                limit=limit,
+            )
         )
-
         if limit is not None:
             # There is a call limit, so just wait for it to finish.
-            await coro
+            await service_task
             return
 
-        # No call limit (i.e., potentially starting one or more fully blocking scripts)
-        # so watch for a stop request.
-        done, pending = await asyncio.wait(
-            {self._stop.wait(), coro}, return_when=asyncio.FIRST_COMPLETED,
-        )
-        # Note that cancelling the service call, if it has not yet returned, will also
-        # stop any non-background script runs that it may have started.
-        for pending_task in pending:
-            pending_task.cancel()
-        # Propagate any exceptions that might have happened.
-        for done_task in done:
-            done_task.result()
+        async def async_cancel_service_task():
+            # Stop service task and wait for it to finish.
+            service_task.cancel()
+            try:
+                await service_task
+            except Exception:  # pylint: disable=broad-except
+                pass
+
+        # No call limit so watch for a stop request.
+        stop_task = self._hass.async_create_task(self._stop.wait())
+        try:
+            await asyncio.wait(
+                {service_task, stop_task}, return_when=asyncio.FIRST_COMPLETED
+            )
+        # If our task is cancelled, then cancel service task, too. Note that if service
+        # task is cancelled otherwise the CancelledError exception will not be raised to
+        # here due to the call to asyncio.wait(). Rather we'll check for that below.
+        except asyncio.CancelledError:
+            await async_cancel_service_task()
+            raise
+        finally:
+            stop_task.cancel()
+
+        if service_task.cancelled():
+            raise asyncio.CancelledError
+        if service_task.done():
+            # Propagate any exceptions that occurred.
+            service_task.result()
+        elif running_script:
+            # Stopped before service completed, so cancel service.
+            await async_cancel_service_task()
 
 
 class _QueuedScriptRun(_ScriptRun):
@@ -459,12 +486,18 @@ class _QueuedScriptRun(_ScriptRun):
         lock_task = self._hass.async_create_task(
             self._script._queue_lck.acquire()  # pylint: disable=protected-access
         )
-        done, pending = await asyncio.wait(
-            {self._stop.wait(), lock_task}, return_when=asyncio.FIRST_COMPLETED
-        )
-        for pending_task in pending:
-            pending_task.cancel()
-        self.lock_acquired = lock_task in done
+        stop_task = self._hass.async_create_task(self._stop.wait())
+        try:
+            await asyncio.wait(
+                {lock_task, stop_task}, return_when=asyncio.FIRST_COMPLETED
+            )
+        except asyncio.CancelledError:
+            lock_task.cancel()
+            self._finish()
+            raise
+        finally:
+            stop_task.cancel()
+        self.lock_acquired = lock_task.done() and not lock_task.cancelled()
 
         # If we've been told to stop, then just finish up. Otherwise, we've acquired the
         # lock so we can go ahead and start the run.