diff --git a/sentry_sdk/integrations/fastapi.py b/sentry_sdk/integrations/fastapi.py
index 3572b1c07f..1c7f20da86 100644
--- a/sentry_sdk/integrations/fastapi.py
+++ b/sentry_sdk/integrations/fastapi.py
@@ -1,4 +1,4 @@
-import asyncio
+import sys
 from copy import deepcopy
 from functools import wraps
 
@@ -32,6 +32,13 @@
 _DEFAULT_TRANSACTION_NAME = "generic FastAPI request"
 
 
+# Vendored: https://github.com/Kludex/starlette/blob/0a29b5ccdcbd1285c75c4fdb5d62ae1d244a21b0/starlette/_utils.py#L11-L17
+if sys.version_info >= (3, 13):  # pragma: no cover
+    from inspect import iscoroutinefunction
+else:
+    from asyncio import iscoroutinefunction
+
+
 class FastApiIntegration(StarletteIntegration):
     identifier = "fastapi"
 
@@ -74,7 +81,7 @@ def _sentry_get_request_handler(*args: "Any", **kwargs: "Any") -> "Any":
         if (
             dependant
             and dependant.call is not None
-            and not asyncio.iscoroutinefunction(dependant.call)
+            and not iscoroutinefunction(dependant.call)
         ):
             old_call = dependant.call
 
diff --git a/sentry_sdk/integrations/starlette.py b/sentry_sdk/integrations/starlette.py
index dac9887e2f..6d28dea3d0 100644
--- a/sentry_sdk/integrations/starlette.py
+++ b/sentry_sdk/integrations/starlette.py
@@ -1,6 +1,6 @@
-import asyncio
 import functools
 import warnings
+import sys
 from collections.abc import Set
 from copy import deepcopy
 from json import JSONDecodeError
@@ -74,6 +74,13 @@
     multipart = None
 
 
+# Vendored: https://github.com/Kludex/starlette/blob/0a29b5ccdcbd1285c75c4fdb5d62ae1d244a21b0/starlette/_utils.py#L11-L17
+if sys.version_info >= (3, 13):  # pragma: no cover
+    from inspect import iscoroutinefunction
+else:
+    from asyncio import iscoroutinefunction
+
+
 _DEFAULT_TRANSACTION_NAME = "generic Starlette request"
 
 TRANSACTION_STYLE_VALUES = ("endpoint", "url")
@@ -424,8 +431,8 @@ def _is_async_callable(obj: "Any") -> bool:
     while isinstance(obj, functools.partial):
         obj = obj.func
 
-    return asyncio.iscoroutinefunction(obj) or (
-        callable(obj) and asyncio.iscoroutinefunction(obj.__call__)
+    return iscoroutinefunction(obj) or (
+        callable(obj) and iscoroutinefunction(obj.__call__)
     )