diff --git a/lib/mechanize/http/agent.rb b/lib/mechanize/http/agent.rb
index 5b1b2266..9e433a3f 100644
--- a/lib/mechanize/http/agent.rb
+++ b/lib/mechanize/http/agent.rb
@@ -9,7 +9,8 @@
 
 class Mechanize::HTTP::Agent
 
-  CREDENTIAL_HEADERS = ['Authorization', 'Cookie']
+  CREDENTIAL_HEADERS = ['Authorization']
+  COOKIE_HEADERS = ['Cookie']
   POST_HEADERS = ['Content-Length', 'Content-MD5', 'Content-Type']
 
   # :section: Headers
@@ -998,10 +999,14 @@ def response_redirect(response, method, page, redirects, headers,
     end
 
     # Make sure we clear credential headers if being redirected to another site
-    if new_uri.host != page.uri.host
-      CREDENTIAL_HEADERS.each do |ch|
-        headers.delete_if { |h| h.casecmp?(ch) }
+    if new_uri.host == page.uri.host
+      if new_uri.port != page.uri.port
+        # https://datatracker.ietf.org/doc/html/rfc6265#section-8.5
+        # cookies are OK to be shared across ports on the same host
+        CREDENTIAL_HEADERS.each { |ch| headers.delete_if { |h| h.casecmp?(ch) } }
       end
+    else
+      (COOKIE_HEADERS + CREDENTIAL_HEADERS).each { |ch| headers.delete_if { |h| h.casecmp?(ch) } }
     end
 
     fetch new_uri, redirect_method, headers, [], referer, redirects + 1
diff --git a/test/test_mechanize_http_agent.rb b/test/test_mechanize_http_agent.rb
index bc8c0580..8a2681f5 100644
--- a/test/test_mechanize_http_agent.rb
+++ b/test/test_mechanize_http_agent.rb
@@ -1569,7 +1569,7 @@ def test_response_redirect_to_cross_site_with_credential
     refute_includes(headers.keys, "AUTHORIZATION")
     refute_includes(headers.keys, "cookie")
 
-    assert_match 'range|bytes=0-9999', page.body
+    assert_match("range|bytes=0-9999", page.body)
     refute_match("authorization|Basic xxx", page.body)
     refute_match("cookie|name=value", page.body)
   end
@@ -1590,11 +1590,32 @@ def test_response_redirect_to_same_site_with_credential
     assert_includes(headers.keys, "AUTHORIZATION")
     assert_includes(headers.keys, "cookie")
 
-    assert_match 'range|bytes=0-9999', page.body
+    assert_match("range|bytes=0-9999", page.body)
     assert_match("authorization|Basic xxx", page.body)
     assert_match("cookie|name=value", page.body)
   end
 
+  def test_response_redirect_to_same_site_diff_port_with_credential
+    @agent.redirect_ok = true
+
+    headers = {
+      'Range' => 'bytes=0-9999',
+      'AUTHORIZATION' => 'Basic xxx',
+      'cookie' => 'name=value',
+    }
+
+    page = html_page ''
+    page = @agent.response_redirect({ 'Location' => 'http://example:81/http_headers' }, :get,
+                                    page, 0, headers)
+
+    refute_includes(headers.keys, "AUTHORIZATION")
+    assert_includes(headers.keys, "cookie")
+
+    assert_match("range|bytes=0-9999", page.body)
+    refute_match("authorization|Basic xxx", page.body)
+    assert_match("cookie|name=value", page.body)
+  end
+
   def test_response_redirect_not_ok
     @agent.redirect_ok = false