Mbesuma, who registered his 10th league goal looked troublesome for the visitors as they failed to deal with strength.
Wits were the first to get on the score-sheet, courtesy of Thulani Hlatswayo, but the lead erased moments later in the first half, after Mbesuma was left unmarked inside the box, before he got the winner for Aces and his second of the match in the second half, after floating came through his way he calmly put the ball through Josephs legs and went in.
Wits started the game brightly, with the first clear chance at goals going their way, when Phakamani Mahlambi skinned Letlhohonolo Nonyane inside the box, but his shot went over the bar.
Two minutes later, Bongolethu Jayiya got a chance to test Moeneeb Josephs, but his shot went wide.
It took only eight minutes for Wits to open the scorings, after a well taken set-piece by Daine Klate found Hlatswayo inside the box, and he cleverly flicked the ball into the net, giving Black Aces keeper Shu-Aib Walters no chance to stop it.
Mbesuma equalised for the visitors in the 16th minute, after Nonyane overlapped on the left side and his low shot cross found the Zambian unmarked inside the box and he placed the ball into the net.
The goal gave Aces some mojo and the visitors started to attack more, with every attack looking dangerous.
But, a miscommunication between their central backs almost gave The Clever Boys another lead, but Mahlambi failed to beat Walters, with the keeper saving the ball with his feet.
Two minutes into second half, Klate had a chance to put Wits on the lead for the second time in the match, but his header unfortunately hit the crossbar.
Aces pulled a counter attacker of their own a minute later, Lebogang Manyama being set free on the right side, but his shot was parred away by Walters.
Aces looked more dangerous between the two sides and they came close to scoring again. This time a mistake by Nazeer Ali inside the box saw Mbesuma winning the ball, but the defender recovered well not to let the veteran to take a shot.
The veteran then got his second goal of the match in the 82nd minute, to take Black Aces to the top of the log, with 30 points.