Stellenboch went ahead after 20 minutes when an unmarked Khomotjo Lekoloane easily tapped into the back of the net a Devin Titus cross.
But eight minutes later, Amakhosi levelled terms through Wandile Duba who headed in a headed pass from Thatayaone Ditlhokwe at close range.
Tactical substitutions by Chiefs on the half-hour mark when coach Nasreddine Nabi took off Bradley Cross and Ashley du Preez for Tebogo Potsane and Mfundo Vilakazi respectively were a reflection of a difficult evening for the Soweto giants.
Duba was back in the 57th minute when he was released by Vilakazi to fire past Stellenbosch goalkeeper Sage Stephens from a tight angle to give the Soweto giants the lead and seal his brace.
It was a perfect 2-1 win for Chiefs on an evening they were celebrating their 55th anniversary
The Soweto giants are now fifth on the log after starting the game at the seventh spot.