The visiting team had taken the lead through Siyabonga Nomvete's first-half added-time goal, but were unable to move off the foot of the table after failing to hold on for the win.
Swallows had the first chance of the game, in the 11th minute, when some great skill from Lerato Chabangu in the SuperSport box ended with him playing a dangerous ball across the face of goal which just eluded Nomvete.
SuperSport though began to take control of the game after that and looked like scoring when Thuso Phala went in clean on goal, but his parting shot kept on rising over the bar.
Jeremy Brockie then had an effort blocked before David Mathebula shot wide as Matsatsantsa continued to stamp their authority on the park.
Swallows were however to come back strongly into the contest as the game moved past the half hour mark, and should have been ahead on 33 minutes.
But having created space in the box with a clever side-step that left him only needing to pick his spot, Felix Obada blasted the ball over the target.
Soon after Nomvete also had an effort on goal as he pulled the trigger with an angled drive from the left, but Ronwen Williams was up to the task.
There was however to be no denying Nomvete as he opened the scoring in first half added time, finishing coolly as he curled the ball past Williams from a tight angle after being played in by Obada's excellent throughpass.
After a fairly quiet start to the second period, it was SuperSport who began to up the ante as they searched out an equaliser.
Brockie had the first chance, but his low free kick on 58 minutes was well dealt with by Sage Stephens, after which the New Zealand international miscued an attempt at the back-post.
Dove Wome then had a go from the edge of the area after taking the ball down on his chest, but his 20-yard volley went just wide of goal.
SuperSport appeared unfortunate not to be awarded an 88th minute penalty after Tsietsi Mahoa looked to have taken down Phala in the box, the Bafana player instead booked for simulation.
But there was no denying the Tshwane side three minutes later as captain Clayton Daniels was given too much time at a corner-kick, allowing him to thud in a 91st minute header.
Vuyisile Wana could have won it late on for Swallows, but sent his shot inches wide of the far post.