The home side were in complete control early on, striking twice before the break through Sanele Barns and Devin Titus.
Though SuperSport showed fight in the second half, they were ultimately kept at bay by a superb performance from Stellenbosch goalkeeper Oscarine Masuluke, who earned Man of the Match honours for a string of decisive saves.
The loss leaves SuperSport 14th on the Betway Premiership table with 26 points, level with fellow strugglers Cape Town City - though Arendse's men still hold a game in hand. That slim margin, however, won't mean much if the inconsistency continues.
Speaking after the match, the Matsatsantsa interim boss didn't hold back in his assessment of his team's poor performance especially in the first-half, but was proud of the team's turn-around in the last period.
"People always say it's a game of two halves - and today, that's exactly what it was. We were nowhere in the first half. It was bordering on embarrassing. The players knew it, and I made sure they knew it," he told SuperSport TV.
"That second-half performance, that's the team I know - full of grit, fight, never giving up. But that kind of spirit was missing when it mattered most."
Still, the former Bafana Bafana goalkeeper knows that character alone won't be enough to survive.
"You can't hand a quality team like Stellenbosch two goals and think you'll chase the game back. They've got quality players, a top coach - and we simply switched off. Those are the moments we need to eliminate if we want to stay in this league," he added.
Matsatsantsa have two games left before the end of season, with their next fixture seeing them go up against Orlando Pirates at Peter Mokaba Stadium on Tuesday.