The Bees got their noses in front early on when Ben Strevens headed home Myles Weston’s cross at the far post with 11 minutes gone.
But the Londoners allowed Walsall to snatch an unlikely point just after the hour mark.
Defender James Wilson let Jones skip away from his challenge and run on to drill a low drive beneath Brentford’s on-loan Arsenal goalkeeper Wojciech Szczesny.
The young Pole then had to be at his best to deny Troy Deeney from claiming all three points for the visitors with a reflex save late on.
But Brentford should have wrapped it up long before half-time with Weston forcing a save from Clayton Ince and John Bostock testing the goalkeeper with a low shot at the near post.