diff --git a/Lib/packaging/tests/test_util.py b/Lib/packaging/tests/test_util.py
--- a/Lib/packaging/tests/test_util.py
+++ b/Lib/packaging/tests/test_util.py
@@ -68,6 +68,16 @@ class FakePopen:
             self.stdout = StringIO(exes[self.cmd])
             self.stderr = StringIO()
 
+    def __enter__(self):
+        return self
+
+    def __exit__(self, type, value, traceback):
+        self.stdout.close()
+        self.stderr.close()
+
+    def communicate(self, input=None, timeout=None):
+        return self.stdout.read(), self.stderr.read()
+
 
 class UtilTestCase(support.EnvironRestorer,
                    support.TempdirManager,
diff --git a/Lib/packaging/util.py b/Lib/packaging/util.py
--- a/Lib/packaging/util.py
+++ b/Lib/packaging/util.py
@@ -465,12 +465,8 @@ def _find_exe_version(cmd, pattern=_RE_V
     executable = cmd.split()[0]
     if find_executable(executable) is None:
         return None
-    pipe = Popen(cmd, shell=True, stdout=PIPE, stderr=PIPE)
-    try:
-        stdout, stderr = pipe.stdout.read(), pipe.stderr.read()
-    finally:
-        pipe.stdout.close()
-        pipe.stderr.close()
+    with Popen(cmd, shell=True, stdout=PIPE, stderr=PIPE) as pipe:
+        stdout, stderr = pipe.communicate()
     # some commands like ld under MacOS X, will give the
     # output in the stderr, rather than stdout.
     if stdout != '':