diff --git a/Lib/test/test_urllib.py b/Lib/test/test_urllib.py
index 673afc42a69..074d833ca47 100644
--- a/Lib/test/test_urllib.py
+++ b/Lib/test/test_urllib.py
@@ -91,7 +91,7 @@ class urlopen_FileTests(unittest.TestCase):
                          "did not return the expected text")
 
     def test_close(self):
-        # Test close() by calling it hear and then having it be called again
+        # Test close() by calling it here and then having it be called again
         # by the tearDown() method for the test
         self.returned_obj.close()
 
@@ -174,6 +174,11 @@ class urlopen_HttpTests(unittest.TestCase):
         finally:
             self.unfakehttp()
 
+    def test_willclose(self):
+        self.fakehttp(b"HTTP/1.1 200 OK\r\n\r\nHello!")
+        resp = urlopen("http://www.python.org")
+        self.assertTrue(resp.fp.will_close)
+
     def test_read_0_9(self):
         # "0.9" response accepted (but not "simple responses" without
         # a status line)
diff --git a/Lib/urllib/request.py b/Lib/urllib/request.py
index 1e437b5b866..4d3648d0f2c 100644
--- a/Lib/urllib/request.py
+++ b/Lib/urllib/request.py
@@ -1657,6 +1657,12 @@ class URLopener:
             headers["Authorization"] =  "Basic %s" % auth
         if realhost:
             headers["Host"] = realhost
+
+        # Add Connection:close as we don't support persistent connections yet.
+        # This helps in closing the socket and avoiding ResourceWarning
+
+        headers["Connection"] = "close"
+
         for header, value in self.addheaders:
             headers[header] = value