Chiefs needed to redeem themselves after their Soweto derby defeat to Orlando Pirates and were looking for an early lead when Siphiwe Tshabalala whipped in a free-kick which Washington Arubi held easily.
Stellenbosch threatened too with a shot from Strijdom Wambi, but it went over the top of Itumeleng Khune’s goal.
Teenage Hadebe came close to the opener with a looping header from a free-kick, but Arubi did well to punch it away for a corner.
The resultant corner led to the opener which Eric Mathoho, returning from injury, headed freely amongst a cluster of defenders on 28 minutes.
Tshabalala looked to secure a second but his in-swinging cross was unable to find any teammates, thus allowing Arubi off his line to punch away the incoming delivery.
Bernard Parker forced Arubi to a one-handed save on the stroke of halftime, with the Zimbabwean stepping up to great effect.
The first period would end in rather satisfactory circumstances for them despite the fact that they had chances aplenty to double their tally.
Steve Komphela’s charges kept up the same energy and intensity after the break, and closed in on a second but Joseph Molangoane could only find the post after rounding Arubi.
A huge ovation preceded the arrival of Hendrick Pule Ekstein, as he replaced a hard-running Wiseman Meyiwa.
After relentless pressure the duration of the game, Leonardo Castro finally got his goal after running onto a through ball to beat Arubi at the near post despite the latter’s prevention efforts.
The Western Cape outfit pulled one back from a corner which Alan Robertson headed home, giving Khune no chance after 77 minutes to set up a grand finish.
The Glamour Boys though managed to sustain the late pressure for a spot in the quarter-final draw set for Thursday evening.
Chiefs: Khune, Cardoso, Mathoho, Hadebe, Zulu, Molangoane, Katsande, Meyiwa (Ekstein 62’), Tshabalala, Parker (Zuma 75’), Castro (Moon 85’).
Subs: Khuzwayo, Ekstein, Paez, Moon, Ntshangase, Zuma, Ngezana.
Stellenbosch: Arubi, Ndlovu (Burds 70’), Barends, Robertson, Georgia (Lark 36’), Nkili, Wambi, Moroole, Rayners, Sithole, Makanda (Mason-Smith 61’).
Subs: Zwane, Burds, Nason-Smith, Lark, Dien, Langeveldt, Pool.