Sim netted in as early as the seventh minute, chipping an on-rushing Itumeleng Khune from inside the box, after being picked out by Bongolwethu Jayiya's cross.
However, the visitors had the first effort on goal a minute earlier when Lewis Macha saw his headed effort saved by Shuaib Walters at his near-post.
After the 10-minute mark, Willard Katsande saw his long-range attempt sail wide of Walters' goal as Chiefs tried to respond quickly and grab the equaliser.
In the 24th minute, a lively William Twala sent in a volleyed cross but Macha arrived seconds too late as it sailed across the face of goal untouched.
The hosts then looked to protect their lead as they dropped deeper into their own half, making it difficult for Chiefs to penetrate into their box, limitting Steve Komphela's side to long-range efforts.
Just before the half-time break Aubrey Modiba tried to pick out Lehlohonolo Majoro at the back-post, but Lorenzo Gordinho did well to cut out the danger with a sliding tackle.
The Soweto giants probed for an equaliser in the sceond half, and demanded teh very best from Walters, who pulled off a man of the match performance to keep his side in the tie.
Twala came closest for the vistors when he hit the upright in the 87th minute.
City advance to their first ever MTN 8 semi-final, as they await the results of the other three encounters.
Kaizer Chiefs have made three changes to their line-up following their Absa Premiership defeat to Bidvest Wits in midweek.
In midfield Lucky Baloyi replaces George Maluleka, while new Zimbabwean signing Edmore Chirambadare is set to make his competitive debut in place of George Lebese, who has been omitted from the squad.
Up front Lewis Macha gets a start alongside Bernard Parker, as Hendrick Ekstein is relegated to the bench.
Meanwhile the hosts have made just two changes from their team that beat Polokwane City 2-0 in their PSL opener on Tuesday.