The defending League champions secured all three points thanks to goals from Excellent Walaza, Elias Pelembe and Brent Carelse, while the visitors from the Eastern Cape will look back on some missed chances that could have changed the complexion of the game.
SuperSport got off to a flying start when, with just 10 minutes of play having elapsed, Walaza met Glen Salmon's misdirected shot and diverted the ball past Arthur Bartman with a well-placed header, scoring his first goal for the club.
Just past the midway point of the first half Shane Poggenpoel set up Walaza with a good cross, but the Umlilo keeper did well to stop the striker's shot, and a few moments later winger Masibusane Zongo blazed a shot over the crossbar.
On the 30-minute mark the hosts almost doubled their lead, as Pelembe got his head on a Zongo free kick from the right flank, but the Mozambican's attempt flashed just wide of the upright.
Bay didn't manage a single effort on target in the first 45 minutes, but their best attempt came from Nhlanhla Vilikazi in the 37th minute – the midfielder was through on goal but Denis Onyango did well to narrow his angle and force the Bay player to shoot wide.
A couple of minutes before the half-time break Walaza again found time and space to get off a shot at the visitors' goal, but Bartman made a fine block to ensure his team was only one goal down at the interval.
After the break SuperSport continued to dominate but Bay should have gained parity early in the second half when Jean Njoh found himself one-on-one with Onyango. Unfortunately for the visitors the keeper made an excellent save.
The Eastern Cape side was punished in the 53rd minute when Pelembe showed some great skill to beat the defence before slotting the ball past Bartman to make it 2-0.
The Tshwane side completed the scoring in the final minute of regulation time when Carelse fired home a fine goal from outside the penalty area.
The result sees Matsatsantsa establish a significant lead in their defence of the Absa Premiership title, though their three closest rivals on the log table, Ajax Cape Town, Kaizer Chiefs and Orlando Pirates, all have a game in hand.