Polokwane City defender Bulelani Nikani beat his own goalkeeper Manuel Sapunga while trying to block Devin Titus' effort to give Stellenbosch the lead 12 minutes into the match.
Then in the 37th minute, Titus' shot struck the post before nestling into the back of the net to double the Cape Winelands' side's advantage.
The 2-0 win saw Stellenbosch advance to the quarter-finals of the Nedbank Cup, eliminating Rise and Shine.