Itumeleng Khune was called into action after 10 minutes as he produced a good save to keep out Amr Gamal's header.
The Clever Boys did all the attacking in the opening exchanges, with Steven Pienaar dictating play from the middle of the park.
Chiefs, on the other hand, were finding it tough to get the ball off Wits in the opening 30 minutes, which led to a lack of chances from their side.
It was proving to be a busy half for Khune, as he produced a double save to deny Daylon Claasen and Gamal after 36 minutes.
With just a few minutes remaining in the second half, the Clever Boys were reduced to 10 men when Nazeer Allie was sent off for a second bookable offence.
Chiefs broke the deadlock after 52 minutes as a great build-up saw Kgotso Moleko pick out Siphiwe Tshabalala to head home from close range.
Wits nearly levelled matters two minutes later, but Vincent Pule's effort from 25 yards out crashed against the crossbar with Khune well beaten.
Gavin Hunt responded by introducing Ben Motshwari, Phumlani Ntshangase and Gabadinho Mhango as they looked for a way back into the clash.
Steve Komphela opted for changes of his own as Keagan Buchanan and Bernard Parker were introduced with 25 minutes remaining.
Despite the numerical disadvantage, the Clever Boys continued to push for an equaliser, although the Chiefs defence were standing firm.
Wits eventually found the equaliser in stoppage time, as Gamal controlled well before firing a fine effort into the bottom corner from the edge of the box.