diff -r 0f663e0ce1d3 Lib/shutil.py
--- a/Lib/shutil.py	Tue Nov 18 17:30:50 2014 +0200
+++ b/Lib/shutil.py	Tue Nov 18 22:13:10 2014 +0200
@@ -617,7 +617,7 @@ def _make_tarball(base_name, base_dir, c
     archive_name = base_name + '.tar' + compress_ext.get(compress, '')
     archive_dir = os.path.dirname(archive_name)
 
-    if not os.path.exists(archive_dir):
+    if archive_dir and not os.path.exists(archive_dir):
         if logger is not None:
             logger.info("creating %s", archive_dir)
         if not dry_run:
@@ -662,7 +662,7 @@ def _make_zipfile(base_name, base_dir, v
     zip_filename = base_name + ".zip"
     archive_dir = os.path.dirname(base_name)
 
-    if not os.path.exists(archive_dir):
+    if archive_dir and not os.path.exists(archive_dir):
         if logger is not None:
             logger.info("creating %s", archive_dir)
         if not dry_run:
diff -r 0f663e0ce1d3 Lib/test/test_shutil.py
--- a/Lib/test/test_shutil.py	Tue Nov 18 17:30:50 2014 +0200
+++ b/Lib/test/test_shutil.py	Tue Nov 18 22:13:10 2014 +0200
@@ -1132,6 +1132,22 @@ class TestShutil(unittest.TestCase):
         finally:
             unregister_archive_format('xxx')
 
+    def test_make_tarfile_in_curdir(self):
+        # Issue #21280
+        root_dir = self.mkdtemp()
+        with support.change_cwd(root_dir):
+            self.assertEqual(make_archive('test', 'tar'), 'test.tar')
+            self.assertTrue(os.path.isfile('test.tar'))
+
+    @requires_zlib
+    @unittest.skipUnless(ZIP_SUPPORT, 'Need zip support to run')
+    def test_make_zipfile_in_curdir(self):
+        # Issue #21280
+        root_dir = self.mkdtemp()
+        with support.change_cwd(root_dir):
+            self.assertEqual(make_archive('test', 'zip'), 'test.zip')
+            self.assertTrue(os.path.isfile('test.zip'))
+
     def test_register_archive_format(self):
 
         self.assertRaises(TypeError, register_archive_format, 'xxx', 1)