Chippa opened the scoring through William Twala from the penalty spot, but second half goals from Bevan Fransman and Bradley Grobler secured all three points for the Tshwane outfit.
Both sides created excellent chances within the space of a minute in the first half.
First, Twala capitalised on some poor defending by Masatsantsa to create a one-on-one situation in the 15th minute of the game, but he could only manage to direct his shot wide of Ronwen Williams’s left-hand upright.
A minute later it was the home side’s turn to squander a gilt-edged chance. Sameehg Doutie did well to dispossess Keamogetse Wolff before playing a precise ball to the feet of Kermit Erasmus, but the striker’s shot was easily gathered by Kassally Daouda.
Benjani Mwaruwari then had an opportunity to open the scoring in the 24th minute. The former Manchester City and Portsmouth striker skipped past a few dismal challenges, but could only blast his effort over the crossbar from close range.
The away side took the lead just after the half hour mark when Twala made up for his earlier miss by planting the ball into the back of the net from the penalty spot, after Grant Kekana brought down Asavela Mbekile inside the area.
SuperSport searched for the equaliser before the half-time whistle but they were unable to penetrate the away side’s defence.
However, 10 minutes after the restart, Fransman rose highest in the box and nodded into the back of the net from a Doutie corner-kick.
Matsatsantsa had a great opportunity to take the lead 15 minutes from time when Thabiso Nkoana played a through ball to Doutie, who cut back to Grobler, but the striker could only manage a tame effort.
He made amends two minutes later, however, heading in from a pin-point Sibusiso Zuma cross to give the home side the lead.
SuperSport held on to move to fourth on the log, and are unbeaten in 13 matches.