diff --git a/sentry_sdk/integrations/stdlib.py b/sentry_sdk/integrations/stdlib.py
index 1aad7a7e9a..2be48a5ba2 100644
--- a/sentry_sdk/integrations/stdlib.py
+++ b/sentry_sdk/integrations/stdlib.py
@@ -459,11 +459,8 @@ def close(self: "HTTPResponse") -> None:
                 self._sentrysdk_span = None  # type: ignore[attr-defined]
                 _complete_span(span)
 
-    HTTPConnection.putrequest = putrequest  # type: ignore[method-assign]
-    # patch `HTTPConnection.putrequest()` first. urllib3 < 1.25.9 inherits it, so
-    # wrapping AWS classes first would skip URL and span recording. Once boto3-v1.16.63
-    # support is dropped, we won't have to worry about this issue.
     _patch_aws_connection()
+    HTTPConnection.putrequest = putrequest  # type: ignore[method-assign]
     HTTPConnection.getresponse = getresponse  # type: ignore[method-assign]
     HTTPResponse.read = read  # type: ignore[method-assign]
     HTTPResponse.close = close  # type: ignore[assignment,method-assign]