Wits dominated the ball possession in the opening exchanges. In the 15th minute Gabadinho Mhango turned well to unleash a drive from the edge of the area however Patrick Tignyemb was untroubled.
Egyptian forward Amr Gamal almost scored the opener but his header from a Reeve Frosler cross sailed just over the crossbar in the 27th minute.
Five minutes before halftime, Slavko Damjanovic almost turned the ball into his own net after his attempt at a clearance went narrowly past Moeneeb Josephs' goal for a corner kick.
Celtic began the second half the more dominant side but they were unable to find the back of the net.
It was proving to be difficult for either team to create clear goal scoring chances as the half wore on.
The home side, however, grabbed the lead after blitzing forward on a counter attack. Former Black Leopards and AmaZulu striker Roggert Nyundu finished off the attack with a tap in 15 minutes from time.
Second half substitute Kobamelo Kodisang tried his luck with a shot from the back post, forcing a good save from Tignyemb, as the visitors went in search of an equaliser.
In the end Celtic held on to collect a vital three points at home.