Mamelodi Sundowns came into the match full of confidence after their 4-1 win over Orlando Pirates in their league game on Saturday.
Lucas Ribeiro, who has now scored seven goals in the league, had his effort come off the upright.
The determined Galaxy got their lone goal in the 44th minute when Denan Zajmovic set up Kamogelo Sebelebele for a clever finish.
Even after the break, Galaxy were determined to defend their win and hit Masandawana on counterattacks. The frustrated Sundowns eventually fell for the third time in the league this season.
The defending champions remain at the summit on 42 points from 16 games, while Galaxy go fourth with 25 points from 17 games.