Sundowns suffered a shock 3-2 loss to a struggling Rockets at the Mbombela Stadium on Tuesday evening.
Victor Letsoalo (6'), Sedwyn George (17') put Galaxy into a two-goal lead before Brayan Leon (37', 40') restored parity before half time.
Mpho Mvelase, however, put the Rockets ahead in the 46th minute and Bernard Parker's side managed to hold on until the final whistle.
The result left the Brazilians top of the standings, but just three points clear of the Buccaneers, who have two games left to play.
Galaxy, meanwhile, ended the evening in 12th place with 31 points from 29 games.
Speaking after the game, a delighted Parker said on SuperSport: "As I said in the pre-match interview because of the psychological factor we have over them.
"At the same time, they were more under pressure by them having to score a lot of goals and having to win the match and it was also good for them to win the match going to play the Champions League final – wish them all the best for the Champions League final.
"But as we say in football we don't have answers but solutions and we came up with a solution in terms of us being disciplined, taking the responsibility and at the same time having the unity especially in our defending and just hit them on the counter-attack because we have been practising on how they keep a high-line and for us just to make sure we attack the space behind.
"At the same time that we continue when I took over on how we wanted to play and we build on that and today it paid fruits for us today.
"So I'm happy that the squad got the belief back we got ourselves back and with the quality Mamelodi Sundowns possess.
“I'm just proud of the boys that they managed to put up a big fight against them.”
