After an opening shot from Ayanda Patosi that flew over the top, City took an early lead after debutant Matthew Rusike got between Thulani Hlatshwayo and Bongani Khumalo to head home Teko Modise’s cross after two minutes.
As expected, the lead drew a response from the Students who pressed forward for the equaliser but it wasn’t forthcoming.
Despite the best efforts of Vincent Pule from a free-kick which went inches wide followed by another misplaced effort moments later, the 2014 finalists struggled to draw level.
With half-time approaching Sifiso Myeni found himself on goal, but he failed to make the most of a promising situation.
Surprisingly, the Citizens made the first change with Craig Martin replacing Patosi who apparently found it tough to get a foothold on the contest.
At the start of the second half, Wits brought on Gabadinho Mhango for Lehlohonolo Majoro as Gavin Hunt fired up their pursuit for the elusive equaliser.
The pressure for the Capetonians continued though, and they were unlucky not to concede after Daylon Claasen saw his attempt cleared off the line by Modise from a corner kick.
A limping Myeni was not to be kept on the field by Hunt who immediately withdrew him in favour of Thabang Monare.
After a clash of heads with Sifiso Hlanti, City were forced to replace Martin for Mozambican-born defender Edmilson, while the Clever Boys made their final change in Thobani Mncwango.
Mhango managed to work a yard of space on the edge of the box, but failed to test Shu-aib Walters who had a pretty comfortable evening in goal.
At the end City made it four wins on the trot against the highly-rated Students as they book a spot in the last 16.