The Clever Boys had previously been beaten by the Citizens in four consecutive fixtures and were eager to buck the trend when they travelled to Cape Town.
After a good start, there was cause for concern when Gabadinho Mango went down injured and was replaced by Vincent Pule.
The hosts were also forced into an early change when Matthew Rusike went down injured.
The half seemed to be drawing to a goalless conclusion when Lehlohonolo Majoro slotted home from close range to hand the visitors the lead.
The hosts came out with a fighting spirit in the second half and were rewarded in the 58th minute, drawing level thanks to a great goal by Craig Martin.
Gavin Hunt’s men, however, were able to bag the winner 17 minutes before time after Mojoro latched onto a Sifiso Hlanti cross to bag his brace and hand the visitors the lead.
The win sees Bidvest Wits move into eighth spot on the Absa Premiership log.