Joseph Molangoane grabbed the opening goal in the 48th minute before Siphiwe Tshabalala added a second 10 minutes later, while Gustavo Paez scored his first goal for the club late on.
Stellenbosch held their own in the first half as they looked an organised outfit, foiling the threat of Chiefs' attack.
Amakhosi came closest to finding the opener in the 32nd minute, when Washington Arubi was forced to react quickly to block a deflected shot from Gustavo Paez.
The hosts had a few good opportunities to threaten the Chiefs defence but were let down by their final pass and decision-making, with a number of efforts from range going wide of the mark.
Similarly on the other end, the Soweto side were restricted to shooting from range but failed to threaten Arubi's goal.
Molangoane broked the deadlock with a easy header into an open net when Gustavo Paez done well to pick out the diminutive winger at the far post with a well-weighted lob.
Tshabalala then doubled Chiefs' lead 10 minutes later when he latched onto a loose ball outside the Stellenbosch area and sent a left-footed strike into the bottom right corner.
Paez got in on the action with a composed finish in the 82nd minute, as he rounded Arubi in a one-on-one before slotting into an empty net.
Stellenbosch XI: Arubi, Skippers (D. Booysen 69'), Sait, Rowell, Brown, Mekoa, Webber (Nene 61'), Mabua, Moroole, Mushond, Dube.
Stellenbosch subs: More, D. Booysen, Nene, Hadebe, Dien, Adonis, De Goede.
Chiefs XI: Khuzwayo, Moleko, Mathoho, Cardoso, Khumalo, Katsande, Baloyi, Molangoane (Lebese 74'), Chirambadare (Twala 63'), Tshabalala, Paez (Ekstein 83').
Chiefs subs: Khune, Gordinho, Mphahlele, Twala, Lebese, Ekstein, Parker.