Petrus Mahlatsi scored a brace for the home team.
Mahlatsi opened the scoring in the 2nd minute with a right-footed strike which beat Moeneeb Josephs, after receiving a neat pass from Thabo Nthethe.
In the 23rd minute Shu-Aib Walters made a great save from a long-range thunderbolt by Almiro Lobo. It was a great chance for Wits to level matters but the keeper managed to parry the shot over for a corner.
Wits had another chance to level matters in the 28th minute when Clive Moyo-Modise had a chance, but Walters reacted quickly to block the ball at the player’s feet.
On the stroke of half time Celtic could have made it 2-0 when they were awarded a penalty, but Moses Spandeel’s effort was saved by Josephs.
Mahlatsi completed his brace in the 48th minute with a left-footed shot this time, beating Josephs on the far left after some lovely build-up work from Mark Mayambela.
The win puts Celtic level on points with Orlando Pirates, although the Soweto side are ahead on goal difference. Pirates lie eleventh, Celtic twelfth, with 36 points a piece. Wits sit just above them with 37.