Vuyisile Ntombayithethi scored the opener for the Chilli Boys half an hour in.
Despite the stifling heat, well over 30 degrees, the action was fast paced and went from end to end early on.
Mbulelo Mabizela headed wide from a corner early on for the visitors, while at the other end, Wits keeper Steven Hoffman did well to keep out low 25-metre strikes from both Cole Alexander and Andile Mbenyane.
It was the Cape side that was posing more questions when pushing forward and they went in front after 30 minutes when Ntombayithethi stole in unmarked to head home Diego Brown's testing free-kick.
Two minutes later Brown was again the provider, but this time Gift Sithole could not convert at the far post.
At the other end, Kassaly Daouda was twice called into action in the home goal, doing very well to keep Sibusiso Vilakazi from scoring on each occasion, clawing the Wits man's volley off the line for the first save.
But Chippa could have added a second goal after 40 minutes if Mbenyane had been more accurate with a header from Brown's cross.
The heat appeared to catch up with the players after the break as the action failed to ignite around either goal box.
The Chilli Boys were then to see their hopes of a first PSL win go up in smoke as former Santos striker Isaacs' sweetly struck shot smashed into the net in the 89th minute, following a corner-kick.
There was almost a late winner for Chippa, but Hoffman rescued his side as he reacted sharply to William Twala's deflected shot and then grabbed the ball away from the onrushing Petrus Ngebo.