diff --git a/providers/sftp/src/airflow/providers/sftp/hooks/sftp.py b/providers/sftp/src/airflow/providers/sftp/hooks/sftp.py
index 1301fd9102cfe..367a8f903973b 100644
--- a/providers/sftp/src/airflow/providers/sftp/hooks/sftp.py
+++ b/providers/sftp/src/airflow/providers/sftp/hooks/sftp.py
@@ -113,8 +113,9 @@ def __init__(
     @contextmanager
     def get_conn(self) -> Generator[SFTPClient, None, None]:
         """Context manager that closes the connection after use."""
-        with closing(super().get_conn().open_sftp()) as conn:
-            yield conn
+        with closing(super().get_conn()) as conn:
+            with closing(conn.open_sftp()) as sftp:
+                yield sftp
 
     def describe_directory(self, path: str) -> dict[str, dict[str, str | int | None]]:
         """
@@ -204,18 +205,18 @@ def create_directory(self, path: str, mode: int = 0o777) -> None:
         :param path: full path to the remote directory to create
         :param mode: int permissions of octal mode for directory
         """
-        with self.get_conn() as conn:
-            if self.isdir(path):
-                self.log.info("%s already exists", path)
-                return
-            elif self.isfile(path):
-                raise AirflowException(f"{path} already exists and is a file")
-            else:
-                dirname, basename = os.path.split(path)
-                if dirname and not self.isdir(dirname):
-                    self.create_directory(dirname, mode)
-                if basename:
-                    self.log.info("Creating %s", path)
+        if self.isdir(path):
+            self.log.info("%s already exists", path)
+            return
+        elif self.isfile(path):
+            raise AirflowException(f"{path} already exists and is a file")
+        else:
+            dirname, basename = os.path.split(path)
+            if dirname and not self.isdir(dirname):
+                self.create_directory(dirname, mode)
+            if basename:
+                self.log.info("Creating %s", path)
+                with self.get_conn() as conn:
                     conn.mkdir(path, mode=mode)
 
     def delete_directory(self, path: str, include_files: bool = False) -> None:
@@ -224,14 +225,18 @@ def delete_directory(self, path: str, include_files: bool = False) -> None:
 
         :param path: full path to the remote directory to delete
         """
+        files: list[str] = []
+        dirs: list[str] = []
+
+        if include_files is True:
+            files, dirs, _ = self.get_tree_map(path)
+            dirs = dirs[::-1]  # reverse the order for deleting deepest directories first
+
         with self.get_conn() as conn:
-            if include_files is True:
-                files, dirs, _ = self.get_tree_map(path)
-                dirs = dirs[::-1]  # reverse the order for deleting deepest directories first
-                for file_path in files:
-                    conn.remove(file_path)
-                for dir_path in dirs:
-                    conn.rmdir(dir_path)
+            for file_path in files:
+                conn.remove(file_path)
+            for dir_path in dirs:
+                conn.rmdir(dir_path)
             conn.rmdir(path)
 
     def retrieve_file(self, remote_full_path: str, local_full_path: str, prefetch: bool = True) -> None:
diff --git a/providers/sftp/tests/provider_tests/sftp/hooks/test_sftp.py b/providers/sftp/tests/provider_tests/sftp/hooks/test_sftp.py
index a35ee4010712d..afed97ba574d5 100644
--- a/providers/sftp/tests/provider_tests/sftp/hooks/test_sftp.py
+++ b/providers/sftp/tests/provider_tests/sftp/hooks/test_sftp.py
@@ -117,6 +117,7 @@ def test_get_close_conn(self, mock_get_conn):
             assert conn == mock_sftp_client
 
         mock_sftp_client.close.assert_called_once()
+        mock_ssh_client.close.assert_called_once()
 
     def test_describe_directory(self):
         output = self.hook.describe_directory(self.temp_dir)