Erick Mathoho’s sixth-minute red card left Chiefs with their backs up against it, and first-half goals from Aubrey Modiba and Bradley Grobler put SuperSport in cruise control.
Amakhosi did manage to ensure a tense second-half, though, after Gustavo Paez scored with 66 minutes gone, although the hosts were unable to complete the comeback as the Soweto giants remain winless this season.
Amakhosi left themselves with a mountain to climb after just six minutes as Mathoho, back-tracking as the last man, ploughed through the back of Grobler on the edge of the area, leaving the referee little chance but to show the defender a red card.
A few minutes later and Matsatsantsa came close to taking advantage of the numbers as Thuso Phala slid through a brilliant ball to find Dove Wome in the area, although the attacker was just off the mark as he curled wide.
However, with 13 minutes gone the visitors stormed into the lead, another piece of slick passing ending with Modiba rising unmarked at the far-post to head back across goal and into the net.
Midway through the first-half and SuperSport had the ball in the back of the net again as Phala hammered home from close range, although the celebrations were cut short by the linesman’s flag for offside.
Ronwen Williams then needed to be sharp to prevent an own goal after a Chiefs corner bounced around in the area before deflecting off Clayton Daniels, with the keeper needing to tip the ball over.
SuperSport would eventually take a two-goal lead into the break as Teboho Mokoena played an inch-perfect through ball for Grobler, who ran through on goal before firing past Brilliant Khuzwayo and into the back of the net.
Chiefs looked to step it up in the second-half, with little to lose for Steve Komphela’s men, and Siphiwe Tshabalala had a good chance to pull a goal back shortly after the hour mark but saw his rasping drive from inside the area tipped over.
Only moments later and Amakhosi got their goal, Tshabalala heading back across goal to find Paez, who had all the space and time in the world to line up his shot and fire home from a few feet out.
The chances started coming thick and fast as the game entered its final 20 minutes, with Phala letting flying from inside the area but shooting straight at the goalkeeper.
Up at the other end and Paez got himself into a great position inside the area but his touch let him down at the vital moment when he otherwise would have been clean through.
Chiefs: Khuzwayo, Mphahlele, Gordinho (Cardoso 17'), Mathoho (sent off 6'), Masilela (Zulu 25'), Maluleka, Katsande, Ekstein, Tshabalala, Parker (Twala 58'), Paez
Unused subs: Bvuma, Buchanan, Zuma, Chirambadare
SSU: Williams, Kekana, Daniels, Gould, Ritchie, Letsholonyane, Mokoena, Phala (Nhlapo 87'), Modiba, Wome (Brockie 46'), Grobler
Unused subs: Pieterse, Mashamaite, Alexander, Mbule, Nkhatha