The only meaningful action of the evening came when Stellenbosch's Mthetheleli Mthiyane collected a second yellow card in the second stanza, reducing the visitors to ten men.
Earlier, much of the early attention centred on the red-hot Jean Lwamba, who came into the encounter having netted six times in his previous four outings. The forward nearly added to that tally in the opening exchanges after cleverly spinning away from Olisah Ndah outside the box before driving a low strike at goal, only for Sage Stephens to react sharply and deny him.
Stellenbosch struggled to create meaningful opportunities during a flat first half, but they almost snatched the lead moments before the interval. Following a corner delivery, that man Ndah found space inside the six-yard box, though his close-range attempt was off target.
After Mthiyane's yellow card, Gavin Hunt shuffled his pack by introducing Langelihle Phili and later Wonderboy Makhubu in an effort to inject energy into the visitorsâ attack.
Phili nearly made an immediate impact after bursting forward and unleashing a fierce long-range effort that looked destined for the top corner, but gloveman Frederick Asare - making only his second appearance between the posts - produced an excellent save to keep the scores level.
Durban City pushed hard in the closing stages and came close through captain Siphamandla Ncanana when he rose to meet a cross from replacement Sasizo Magawana, but failed to find the target.