Wits started quite slow, but grew after the 10th minute when Terrence Dzvukamanja got the first shot in anger after a ball from Sifiso Hlanti.
The visitors were left dangling in sixes and sevens when Haashim Domingo found Xolani Machupu who finished easily only for the officials to rule it for offside on 25 minutes.
Seconds later, a similar scenario unfolded which Machupu at the end of a loose ball and managed to found the net only for the linesman on this occasion to rule it for offside.
Following a nice first touch from Domingo, he drove towards goal before taking aim but good defending from amongst others Clayton Daniels prevented the effort from testing Ronwen Williams.
A change from the Students got the second half off the mark, as Bantu Mzwakali replaced Hotto for apparent tactical reasons.
SuperSport conceded a free-kick just outside the box, but Thabang Monare was unable to beat Williams after 59 minutes as the keeper pulled out a stunning save.
After a slow passage of play which brought a limited amount of chances, SuperSport took an early lead after the midway stage.
Zimbabwean marksman Evans Rusike capitalised on slack defending to poke home from close range after 71 minutes.
That was all it took for United to grab their first triumph on the road this season to move in the top-three while at it.