Chiefs needed a last-gasp winner from Itumeleng Shopane to go with strikes from Tristan Moses and Yusuf Bunting, who also missed a penalty in the MultiChoice Diski Challenge contest in Soweto.
The result lifted Zwane's side to sixth on the MDC standings with 19 points from 13 games - 10 points adrift of leaders Golden Arrows with two matches left.
“We created so many chances that we should have scored more,” Zwane told his club's website.
“We raided their box so many times. Stars only got to our box when they scored. We were in control of the match. Besides that, we also missed a penalty.”
He added: “We could have finished the match in regulation time. We knew Stars were going to tire under the heat. We made it difficult for ourselves as we had the game firmly under control.
“It is all part of the development process on which we continuously work. I am happy with the win.”