Aubrey Ngoma's cross at the death forced an own-goal from Musa Bilankulu in the Mother City.
City talisman Lebogang Manyama also earned a late penalty, but the star attacker failed to convert his attempt for the Telkom Knockout winners.
Eric Tinkler's team have now qualified for the CAF Confederation Cup and could yet snipe second spot from Mamelodi Sundowns - behind new champions Bidvest Wits - when they meet Polokwane City on the final day of the campaign on May 27.
Abafana Bes'thende are still in contention for a top-eight berth - and entry to next term's MTN8 - going into their last league tie with Orlando Pirates.
Clinton Larsen's charges will first meet Pirates in the Nedbank Cup semi-finals at Princess Magogo Stadium on Sunday.