Dove Wome, Kingston Nkhatha and Jeremy Brockie scored the goals for the visitors. Arrows ended the game with 10 men following Siyabonga Dube's dismissal for a second bookable offence.
SuperSport were on the front foot from the first whistle and after Thuso Phala's deflected shot whistled past the face of goal, Wome struck home the opener on four minutes.
The Togo international started the attack and after brilliant one-touch passing by fellow attackers Jeremy Brockie, Nkhatha and Thuso Phala - who slipped the ball in behind the Arrows defence - Wome fired past Maximilian Mbaeva.
Matsatsantsa were all over their opponents in the opening half-hour and doubled their lead in the 29th minute from the penalty spot.
The referee awarded the visitors a spot-kick after Chris Katjiukua was adjudged to have pulled back Clayton Daniels inside the area. Nkhatha duly stepped up, guiding the ball past Mbaeva.
Abafana Bes’thende created very little going forward, with their best chance of the match coming in the 64th minute. Kudakwashe Mahachi had Ronwen Williams beaten, but not Mario Booysen, who cleared the danger off the line.
Things went from bad to worse for the hosts eight minutes later, Dube sent off for a silly infringement, much to the disapproval of his head coach.
Brockie then scored his 10th League goal of the season, tapping in from a Michael Morton cross with three minutes remaining.