Swallows showed great tenacity and were the better side in the first-half, encouraging signs for Greg Etafia and his troops who are bottom of the National First Division, and in real danger of relegation.
The proud Soweto outfit tested Ronwen Williams in the 17th minute through Edwin Sitayitayi - the Dube Birds striker forcing the SuperSport keeper into a double save.
Jeremy Brockie scored the decisive goal for Matsatsantsa in the 52nd minute; the New Zealand international's 13th goal of the season moving him top of the scoring charts in all competitions - having also scored in the MTN8, Telkom Knockout and Absa Premiership this season.
Dove Wome teed up Brockie who directed a curling shot past the outstretched Aubrey Mathibe and into the top corner.
Swallows tried in vain to mount a comeback with the evergreen Josta Dladla beating the offside trap before dragging his shot wide of goal on the hour-mark.
SuperSport saw out the rest of the game with relative ease to progress to the next round, where the following teams await: cup holders Mamelodi Sundowns, Jomo Cosmos, Polokwane City, Mpumalanga Black Aces, Baroka FC, Mbombela United, Golden Arrows, University of Pretoria, Free State Stars, Orlando Pirates, Bidvest Wits, Platinum Stars, Santos, Maritzburg United and Magesi FC.
SuperSport XI: Williams, Daniels, Furman, Nkhatha, Brockie, Wome, Morton, Kekana, Mpeta, Booysen, Rambuwane.