Index: Lib/tarfile.py
===================================================================
--- Lib/tarfile.py	(revision 67926)
+++ Lib/tarfile.py	(working copy)
@@ -1707,7 +1707,7 @@
 
         try:
             t = cls.taropen(name, mode,
-                gzip.GzipFile(name, mode, compresslevel, fileobj),
+                gzip.GzipFile(os.path.basename(name), mode, compresslevel, fileobj),
                 **kwargs)
         except IOError:
             raise ReadError("not a gzip file")