His deflected shot cancelled out Dean Sinclair's first-half volley as the Saddlers fought their way back into a game they looked out of at the break.
He connected well with substitute Carlos Fangueiro to drill the ball low and hard, with the aid of a deflection past home keeper Lee Harrison.
Boss Richard Money's half-time team talk made the difference as Walsall came out on the attack.
But it was Barnet who had controlled the game during the first period.
Captain Ian Hendon linked up well with Barry Cogan down the right launching long balls down field which caused the visitors numerous problems.
And on 16 minutes it was Hendon's long throw which Anthony Charles flicked on for Sinclair to volley home at point-blank range.
Tresor Kandol, the subject of a failed £150,000 bid from Brighton this week, wasted a number of chances to increase Barnet's lead.
Just before the break, Hendon, returning from a bruised toe, fed the ball to Cogan who crossed for Kandol, but again he failed to get a proper connection on the ball.
Walsall looked more lively after the break and Martin Butler soon had a chance to get back into the game but keeper Harrison raced out to block his shot.
The experienced Keates got the scores level on 58 minutes when his 20-yard drive deflected into the net following a Fangueiro cross.
Butler almost made it two a minute later but Harrison saved well.
Barnet quickly went down the other end with Jason Puncheon seeing his effort cleared on the line by keeper Clayton Ince.
The game opened up despite the blustery conditions but neither side could grab the winner.
Puncheon saw another effort saved 15 minutes from time, after beating two Saddlers defenders.
And visitors' substitute Mark Wright had his shot bundled off the line by Simon King after Harrison parried Ishmael Demontagnac's blast.
Chris Westwood hit the bar on moments later for the home side, but the scores remained level up the final whistle.