Shaun Bartlett and substitute David Obua scored the goals to secure the crucial points for the Amakhosi.
The visitors made their intentions clear from the offset and were rewarded in the 12th minute when the impressive Onismor Bhasera crossed from the left for former Bafana Bafana striker Shaun Bartlett to head home.
Chiefs should have doubled their lead in the 18th minute when Bartlett shot wide of goal from close range, after latching onto a good cross by winger Arthur Zwane.
The hosts struggled to breach the Amakhosi defence, so much so, that they were forced to resort to long range efforts on Itumeleng Khune’s goal, none which seriously threatened Chiefs.
The first real chance for the Students arrived in the 34th minute when Phil Evans saw his shot cleared off the line by Mokete Tsotetsi, following a good build-up by the hosts.
The score remained 1-0 at the break.
BidVest Wits looked a much improved side in the second half when and should have leveled matters in the 71st minute when substitute Samuel Senokoane missed from close range after receiving a good pass from Clive Moyo-Modise.
The effort by the hosts seemed to spur Chiefs into action as they then piled the pressure on Moeneeb Josephs’ goal, with the Bafana Bafana keeper pulling off a superb save to deny Kaizer Motaung Jnr in the 74th minute.
However, there was not much Josephs could do when Obua slotted home from inside the area after latching onto a good pass by Bhasera.