The game got off to a slow start but then suddendly burst into life after 10 minutes when Leonardo Castro opened his Sundowns account, turning home a low cross from the right from Themba Zwane.
Just moments prior to that Bongani Zungu had a goal disallowed for an apparent handball, although replays should the decision may have been incorrect.
But there was no time to dwell on anything as David Mathebula pulled SuperSport level just three minutes later, curling in a spectacular direct free-kick into the top-left corner from 25 yards out.
Castro had the ball in the back of the net again in the 38th minute but was then booked for handball. The Colombian striker put his hands up to protect his face as Ronwen Williams cleared a Zungu cross but also diverted the ball over the goal-line. Zungu was not booked for his apparent handball goal after just nine minutes played.
After an uneventful start to the second stanza, the Brazilians breathed life into the contest again with a headed goal from Thabo Nthethe, who shook off the attentions of Jeremy Brockie and powered home Keagan Dolly's cross at the far post from close range.
Pitso Mosimane's side continued to threaten on the counter-attack as Matsatsanta pushed for an equaliser and the third and game-clinching goal came in the 80th minute via Zungu, who produced a superb solo run down the left flank, skipped past the first man and then past Clayton Daniels before composing himself and slotting into the bottom-right corner.
Sundowns will take on Chiefs in the Final on December 16 after Amakhosi edged Orlando Pirates on penalties in the first semi-final.