diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 6769066cabd..1fae29430fe 100755
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -420,6 +420,8 @@ def _init_write_gz(self):
         self.__write(b"\037\213\010\010" + timestamp + b"\002\377")
         if self.name.endswith(".gz"):
             self.name = self.name[:-3]
+        # Honor "directory components removed" from RFC1952
+        self.name = os.path.basename(self.name)
         # RFC1952 says we must use ISO-8859-1 for the FNAME field.
         self.__write(self.name.encode("iso-8859-1", "replace") + NUL)
 
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 4ef20db0971..7b34d53d216 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -1417,12 +1417,15 @@ def write(self, data):
                                    pax_headers={'non': 'empty'})
             self.assertFalse(f.closed)
 
+
 class GzipWriteTest(GzipTest, WriteTest):
     pass
 
+
 class Bz2WriteTest(Bz2Test, WriteTest):
     pass
 
+
 class LzmaWriteTest(LzmaTest, WriteTest):
     pass
 
@@ -1465,8 +1468,17 @@ def test_file_mode(self):
         finally:
             os.umask(original_umask)
 
+
 class GzipStreamWriteTest(GzipTest, StreamWriteTest):
-    pass
+    def test_source_directory_not_leaked(self):
+        """
+        Ensure the source directory is not included in the tar header
+        per bpo-41316.
+        """
+        tarfile.open(tmpname, self.mode).close()
+        payload = pathlib.Path(tmpname).read_text(encoding='latin-1')
+        assert os.path.dirname(tmpname) not in payload
+
 
 class Bz2StreamWriteTest(Bz2Test, StreamWriteTest):
     decompressor = bz2.BZ2Decompressor if bz2 else None
diff --git a/Misc/ACKS b/Misc/ACKS
index a2cdeb85040..8b0d7a45da1 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -242,6 +242,7 @@ Colm Buckley
 Erik de Bueger
 Jan-Hein Bührman
 Lars Buitinck
+Artem Bulgakov
 Dick Bulterman
 Bill Bumgarner
 Jimmy Burgett
diff --git a/Misc/NEWS.d/next/Library/2020-07-28-12-08-58.bpo-41316.bSCbK4.rst b/Misc/NEWS.d/next/Library/2020-07-28-12-08-58.bpo-41316.bSCbK4.rst
new file mode 100644
index 00000000000..139a170866e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-07-28-12-08-58.bpo-41316.bSCbK4.rst
@@ -0,0 +1 @@
+Fix the :mod:`tarfile` module to write only basename of TAR file to GZIP compression header.
\ No newline at end of file