diff --git a/sdk/core/azure-core/azure/core/pipeline/transport/requests_basic.py b/sdk/core/azure-core/azure/core/pipeline/transport/requests_basic.py
index 95757edb63dd..d18d63a436f1 100644
--- a/sdk/core/azure-core/azure/core/pipeline/transport/requests_basic.py
+++ b/sdk/core/azure-core/azure/core/pipeline/transport/requests_basic.py
@@ -246,7 +246,7 @@ def send(self, request, **kwargs): # type: ignore
                 allow_redirects=False,
                 **kwargs)
 
-        except urllib3.exceptions.NewConnectionError as err:
+        except (urllib3.exceptions.NewConnectionError, urllib3.exceptions.ConnectTimeoutError) as err:
             error = ServiceRequestError(err, error=err)
         except requests.exceptions.ReadTimeout as err:
             error = ServiceResponseError(err, error=err)
diff --git a/sdk/core/azure-core/tests/test_pipeline.py b/sdk/core/azure-core/tests/test_pipeline.py
index e9df06b0d72a..0c8df68e03bd 100644
--- a/sdk/core/azure-core/tests/test_pipeline.py
+++ b/sdk/core/azure-core/tests/test_pipeline.py
@@ -58,7 +58,7 @@
     RequestsTransport
 )
 
-from azure.core.configuration import Configuration
+from azure.core.exceptions import AzureError
 
 
 def test_sans_io_exception():
@@ -107,6 +107,20 @@ def test_basic_requests(self):
         assert pipeline._transport.session is None
         assert response.http_response.status_code == 200
 
+    def test_requests_socket_timeout(self):
+        conf = Configuration()
+        request = HttpRequest("GET", "https://bing.com")
+        policies = [
+            UserAgentPolicy("myusergant"),
+            RedirectPolicy()
+        ]
+        # Sometimes this will raise a read timeout, sometimes a socket timeout depending on timing.
+        # Either way, the error should always be wrapped as an AzureError to ensure it's caught
+        # by the retry policy.
+        with pytest.raises(AzureError):
+            with Pipeline(RequestsTransport(), policies=policies) as pipeline:
+                response = pipeline.run(request, connection_timeout=0.000001)
+
     def test_basic_requests_separate_session(self):
 
         session = requests.Session()