The only goal of the game was scored early in the second half by Malawian international striker Gabadinho Mhango.
The match is being played in Dobsonville due to the risk of protest disruption at The Clever Boys' regular stadium contained within Wits University.
Mashego almost marked his Chippa debut with a goal when a poor back-pass from Thulani Hlatshwayo was intercepted by the veteran forward, but he could only put his effort into the side-netting.
The home side lost Xolani Mlambo just after the half-hour mark to be replaced by Ben Motshwari.
Mhango had a good chance to grab the lead for Wits late in the first half when his got a powerful shot off, but Daniel Akpeyi in the Chippa goal produced a good stop.
Mhango did give Wits the lead nine minutes after the break when he headed home a Elias Pelembe cross to score his second in as many games.