Seluleko Mahlambi netted his sixth goal of the 2025/26 campaign with a header after just 10 minutes and the result was sealed when Sanele Barns bundled the ball into his own net in the dying minutes of the match.
Rockets boss Adnan Beganovic made two changes from the side that lost 2-1 to Golden Arrows in the Carling Knockout with Mzwandile Dlamini and Solomon Letsoenyo selected.
Stellies, meanwhile, recalled Sage Stephens, Barns, and Lehlohonolo Mojela from their 4-0 cup loss to Marumo Gallants.
It took just 10 minutes for Galaxy to heap more misery on a struggling Stellenbosch as Mahlambi headed home a Puso Dithejane delivery.
Ira Tape was kept busy in the opening period, with Mojela Lehlohonolo the closest to testing the Galaxy goalkeeper, who was forced into a strong save.
Stellies coach Steve Barker introduced Lesiba Nku for Devon Titus and Mthetheleli Mthiyane for Khomotjo Lekoloane in a bid to force a way back into the tie.
But it was Galaxy who dominated the chances in front of goal and Junior Zindonga should have added a second, but he underhit his effort and it was cleared off the line.
Lekoloane got a shot away, but Stephens was equal to it, while the three points were ultimately sealed when Barns inadvertently directed a Mahlambi ball into this own net.
The result saw Galaxy move onto 16 points in sixth place from ten games and leave Stellies in 14th place with nine points from 11 games, three clear of bottom-side Chippa United.
Golden Arrows, meanwhile, thrashed Golden Arrows 4-0 at the King Goodwill Zwelithini Stadium.
Junior Dion opened the scoring on 15 minutes. It took until the 70th minute for Arrows to double their lead as Isaac Cisse fired home. Thokozani Khumalo then netted a late brace, in the 86th and 92nd minutes.
For Arrows it was a second win in a row aftrer their 2-1 Carling Knockout win over TS Galaxy and a fifth win in six matches across all competitions,
The result left them in seventh place on the Betway Premiership standings with 16 points from 11 games.
Gallants are down in 10th with 13 points. They were 4-0 winners last time, eliminating Stellies from the Carling Knockout.
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