The Clever Boys had taken a 2-0 lead into the break after scoring two quick-fire goals. The men from Pietermaritzburg showed character in the second half and were back in contention when Mohau Mokate grabbed a goal back 20 minutes from time, but league leaders Wits were able to hang on doggedly for victory.
The visitors had the first chance of the night when a mistake at the back gave Simon Murray a chance, but the Clever Boys marksman shot wide.
In what was a tight first half, the contest for the most part took part in the engine room where the Team of Choice worked hard to try and get a grip of the game.
Maritzburg created a chance midway through the first stanza when Fortune Makaringe combined nicely with Siphesihle Ndlovu, but failed to find the target with his shot.
Having worked hard to try and take command of the match, United suffered a setback in the 39th minute when Hashim Domingo's shot from the edge of the area was deflected in for an own goal by Nazeer Allie.
The defending Telkom Knockout champions extended their advantage six minutes later when Buhle Mkhwanazi climbed above everyone to thump in a header from Elias Pelembe's corner kick.
Maritzburg began the second half full of purpose and some excellent play on the hour mark enabled Yannick Zakri to get in a shot, but Clever Boys keeper Darren Keet got down well to make the save.
The home side kept on looking for an opener and it took a superb sliding tackle from Wits defender Robyn Johannes to keep out Mohau Mokate's 68th minute shot, before Mokate had a header saved from the resultant corner.
There was no denying the Team of Choice as they made the pressure count when Justice Figuaredo got on the score-sheet in the 71st minute, sweeping in a very well taken first time shot after Ndlovu’s initial effort had been blocked.
The wind firmly in their sails and backed by a lively home crowd, United went pouring forward for another goal.
But it just would not fall for them as the Students defended resolutely to book their spot in the semi-finals.
Maritzburg: Mpandle, Thlone, Xulu, Shandu, Allie, Mekoa, Sanoka, Makaringe, Zakri, Ndlovu, Mokate.
Subs: Ofori, De Reuck, Kunene, Onyango, Figareido, Makgalwa, Fileccia.
Wits: Keet, Hlatshwayo, Johannes, Monare, Murray, Hotto, Hlanti, Mkhwanazi, Alexander, Domingo, Dzvukamanja.
Subs: Mere, Weidlich, Pelembe, Motupa, Ritchie, Macuphu.
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