Subusiso Vilakazi opened the scoring for Wits before Aubrey Ngoma levelled matters just before the break with a superb free-kick. Faty, though, secured all three points for the Clever Boys.
Veteran goalkeeper Andre Arendse started in goal for Wits due to injury problems. The former Bafana Bafana keeper did well to deny Lionel Mutizwa in the 28th minute. The Zimbabwean hit a stinging drive at goal but the Wits shot stopper was up to the task.
Wits opened the scoring in the 36th minute. Vilakazi pounced on a loose ball in the area to bag his fourth goal of the season. Washington Arubi did well to save Calvin Kadi's initial effort, but could do nothing to deny the Wits captain.
AmaTuks, though, didn't take long to level matters. Aubrey Ngoma curled a free-kick into the back of the net past a helpless Arendse five minutes before the break. The goal was the midfielder's sixth of the campaign.
Despite the early indications that it would be a night for the defenders, the game opened up towards the end of the first-half. The teams went into the break deadlocked at 1-1.
Like the first 45, the second started off at a slow pace but picked up momentum as the game wore on.
Vilakazi thought he had bagged a brace in the 64th minute of the game, but the midfielder was adjudged to be off-side.
AmaTuks took full advantage of the Wits players protesting to the official and nearly scored on the resulting counter-attack.
The Clever Boys, though, restored their one goal lead thanks to Faty in the 75th minute. Vilakazi and Kadi linked up well before the latter played a square ball to the Burundian, who in turn slotted the ball past Arubi.
AmaTuks went desperately in search of the equaliser in the final few minutes but the Clever Boys' defence stood tall.