Ryan Moon had given the home team the ideal start when he scored within three minutes. But despite an early onslaught they were unable to add to their tally.
Celtic came back strongly in the second half and found the equaliser through Mzwanele Mahashe, before Ndumiso Mabena scored a long-range winner in the 81st minute.
Stellenbosch coach Steve Barker says he thought his team were in control in the first half, but admits that Celtic were the better team in the second half.
Barker says he had hoped his team could still find a late equaliser, but in the end Celtic were just sharper, and they now need to focus on game away to Highlands Parks on Saturday.
Celtic coach Lehlohonolo Seema says that it was a tough first half as Stellenbosch came at them strongly.
But Seema says they were confident they could come back against a tiring Stellenbosch side, and he made tactical changes that paid off.
– Report by Tshenolo Meruti