diff --git a/overlay/tio/queueset_poll_linux.go b/overlay/tio/queueset_poll_linux.go
index ab967df4..016baf6d 100644
--- a/overlay/tio/queueset_poll_linux.go
+++ b/overlay/tio/queueset_poll_linux.go
@@ -48,11 +48,15 @@ func (c *pollQueueSet) Add(fd int) error {
 func (c *pollQueueSet) wakeForShutdown() error {
 	var buf [8]byte
 	binary.NativeEndian.PutUint64(buf[:], 1)
-	_, err := unix.Write(int(c.shutdownFd), buf[:])
+	_, err := unix.Write(c.shutdownFd, buf[:])
 	return err
 }
 
 func (c *pollQueueSet) Close() error {
+	if c.shutdownFd < 0 {
+		return nil
+	}
+
 	errs := []error{}
 
 	if err := c.wakeForShutdown(); err != nil {
@@ -65,5 +69,12 @@ func (c *pollQueueSet) Close() error {
 		}
 	}
 
+	// All Polls reference shutdownFd in their pollfd arrays, so close it
+	// only after every Poll.Close has returned.
+	if err := unix.Close(c.shutdownFd); err != nil {
+		errs = append(errs, err)
+	}
+	c.shutdownFd = -1
+
 	return errors.Join(errs...)
 }
diff --git a/overlay/tio/tun_file_linux_test.go b/overlay/tio/tun_file_linux_test.go
index f92f58ec..41fe32e5 100644
--- a/overlay/tio/tun_file_linux_test.go
+++ b/overlay/tio/tun_file_linux_test.go
@@ -80,3 +80,24 @@ func TestPoll_Close_Idempotent(t *testing.T) {
 		t.Fatalf("second Close should be a no-op, got %v", err)
 	}
 }
+
+func TestPollQueueSet_Close_ClosesEventfd(t *testing.T) {
+	qs, err := NewPollQueueSet()
+	require.NoError(t, err)
+	require.NoError(t, qs.Add(newReadPipe(t)))
+
+	fd := qs.(*pollQueueSet).shutdownFd
+	require.NoError(t, qs.Close())
+
+	// Closing the eventfd again should fail with EBADF, proving Close
+	// actually released it.
+	if err := unix.Close(fd); err == nil {
+		t.Fatalf("eventfd %d still open after QueueSet.Close", fd)
+	}
+
+	// Second Close must be a no-op (and must not double-close the eventfd
+	// in case the kernel handed it out to another caller in the meantime).
+	if err := qs.Close(); err != nil {
+		t.Fatalf("second Close: %v", err)
+	}
+}