diff --git a/sdk/core/azure-core/tests/async_tests/test_rest_headers_async.py b/sdk/core/azure-core/tests/async_tests/test_rest_headers_async.py
index 7fcf6c153fc2..3b61c59b69d5 100644
--- a/sdk/core/azure-core/tests/async_tests/test_rest_headers_async.py
+++ b/sdk/core/azure-core/tests/async_tests/test_rest_headers_async.py
@@ -12,6 +12,7 @@
 
 # flask returns these response headers, which we don't really need for these following tests
 RESPONSE_HEADERS_TO_IGNORE = [
+    "Connection",
     "Content-Type",
     "Content-Length",
     "Server",
@@ -24,7 +25,7 @@ async def _get_response_headers(request):
         response = await client.send_request(request)
         response.raise_for_status
         for header in RESPONSE_HEADERS_TO_IGNORE:
-            response.headers.pop(header)
+            response.headers.pop(header, None)
         return response.headers
     return _get_response_headers
 
diff --git a/sdk/core/azure-core/tests/test_rest_headers.py b/sdk/core/azure-core/tests/test_rest_headers.py
index cc2f564e70c1..db77b9751cfb 100644
--- a/sdk/core/azure-core/tests/test_rest_headers.py
+++ b/sdk/core/azure-core/tests/test_rest_headers.py
@@ -21,6 +21,7 @@ def _get_request_headers(header_value):
 
 # flask returns these response headers, which we don't really need for these following tests
 RESPONSE_HEADERS_TO_IGNORE = [
+    "Connection",
     "Content-Type",
     "Content-Length",
     "Server",
@@ -33,7 +34,7 @@ def _get_response_headers(request):
         response = client.send_request(request)
         response.raise_for_status
         for header in RESPONSE_HEADERS_TO_IGNORE:
-            response.headers.pop(header)
+            response.headers.pop(header, None)
         return response.headers
     return _get_response_headers