diff --git a/uvicorn/protocols/http/h11_impl.py b/uvicorn/protocols/http/h11_impl.py
index 89e550229..556b94f2e 100644
--- a/uvicorn/protocols/http/h11_impl.py
+++ b/uvicorn/protocols/http/h11_impl.py
@@ -145,6 +145,7 @@ def connection_lost(self, exc: Optional[Exception]) -> None:
             self.flow.resume_writing()
         if exc is None:
             self.transport.close()
+            self._unset_keepalive_if_required()
 
     def eof_received(self) -> None:
         pass
diff --git a/uvicorn/protocols/http/httptools_impl.py b/uvicorn/protocols/http/httptools_impl.py
index d9f294129..5035ec935 100644
--- a/uvicorn/protocols/http/httptools_impl.py
+++ b/uvicorn/protocols/http/httptools_impl.py
@@ -137,6 +137,9 @@ def connection_lost(self, exc: Optional[Exception]) -> None:
             self.flow.resume_writing()
         if exc is None:
             self.transport.close()
+            self._unset_keepalive_if_required()
+
+        self.parser = None
 
     def eof_received(self) -> None:
         pass