City made the brighter start and Koapeng was denied by Ngobeni after an excellent run from Lebogang Manyama.
Ngobeni then stretched out a leg to deny Aubrey Ngoma a goal, before the diminutive winger took too long to get his shot away after being played in by Moseamedi just before halftime.
It was more of the same in the second half, with Stars having to rely on half-chances on the break, and City pushing hard for the opening goal.
That finally arrived on 62 minutes when right-back Vincent Kobola got to the byline and supplied a cross that was headed home by the lively Moseamedi.
It should have been 2-0 just minutes later when Moseamedi turned provider for Ngoma again, but the winger’s goal-bound shot from 10-yards was brilliantly saved by Ngobeni.
Sinethemba Jantjie tested the palms of home goalkeeper Shu-Aib Walters from a free-kick, but it was comfortable in the end for the gloveman, which was about as close as the visitors came in the game.