diff --git a/requests/sessions.py b/requests/sessions.py
index a0a23ee..9a51f33 100644
--- a/requests/sessions.py
+++ b/requests/sessions.py
@@ -18,7 +18,7 @@ from .cookies import (
     cookiejar_from_dict, extract_cookies_to_jar, RequestsCookieJar, merge_cookies)
 from .models import Request, PreparedRequest, DEFAULT_REDIRECT_LIMIT
 from .hooks import default_hooks, dispatch_hook
-from .utils import to_key_val_list, default_headers, to_native_string
+from .utils import to_key_val_list, default_headers, to_native_string, DEFAULT_PORTS
 from .exceptions import (
     TooManyRedirects, InvalidSchema, ChunkedEncodingError, ContentDecodingError)
 from .packages.urllib3._collections import RecentlyUsedContainer
@@ -103,8 +103,17 @@ class SessionRedirectMixin(object):
         if (old_parsed.scheme == 'http' and old_parsed.port in (80, None)
                 and new_parsed.scheme == 'https' and new_parsed.port in (443, None)):
             return False
+
+        # Handle default port usage corresponding to scheme.
+        changed_port = old_parsed.port != new_parsed.port
+        changed_scheme = old_parsed.scheme != new_parsed.scheme
+        default_port = (DEFAULT_PORTS.get(old_parsed.scheme, None), None)
+        if (not changed_scheme and old_parsed.port in default_port
+                and new_parsed.port in default_port):
+            return False
+
         # Standard case: root URI must match
-        return old_parsed.port != new_parsed.port or old_parsed.scheme != new_parsed.scheme
+        return changed_port or changed_scheme
 
     def resolve_redirects(self, resp, req, stream=False, timeout=None,
                           verify=True, cert=None, proxies=None):
diff --git a/requests/utils.py b/requests/utils.py
index 8fba62d..14c94bd 100644
--- a/requests/utils.py
+++ b/requests/utils.py
@@ -37,6 +37,8 @@ NETRC_FILES = ('.netrc', '_netrc')
 
 DEFAULT_CA_BUNDLE_PATH = certs.where()
 
+DEFAULT_PORTS = {'http': 80, 'https': 443}
+
 
 def dict_to_sequence(d):
     """Returns an internal sequence dictionary update."""
diff --git a/test_requests.py b/test_requests.py
index e19b436..b76d2a4 100755
--- a/test_requests.py
+++ b/test_requests.py
@@ -1012,6 +1012,17 @@ class RequestsTestCase(unittest.TestCase):
         s = requests.Session()
         assert s.should_strip_auth('http://example.com:1234/foo', 'https://example.com:4321/bar')
 
+    @pytest.mark.parametrize(
+        'old_uri, new_uri', (
+            ('https://example.com:443/foo', 'https://example.com/bar'),
+            ('http://example.com:80/foo', 'http://example.com/bar'),
+            ('https://example.com/foo', 'https://example.com:443/bar'),
+            ('http://example.com/foo', 'http://example.com:80/bar')
+        ))
+    def test_should_strip_auth_default_port(self, old_uri, new_uri):
+        s = requests.Session()
+        assert not s.should_strip_auth(old_uri, new_uri)
+
     def test_manual_redirect_with_partial_body_read(self):
         s = requests.Session()
         r1 = s.get(httpbin('redirect/2'), allow_redirects=False, stream=True)