Victor Letsoalo, Sedwyn George put Galaxy into a two-goal lead before Brayan Leon restored parity before half time.
Mpho Mvelase, however, put the Rockets ahead in the 46th minute and they managed to hold that lead until the final whistle.
The result put the Betway Premiership title race firmly in Orlando Pirates’ hands, who are three points behind the current South African top-flight champions – with two games in hand.
Sundowns have completed their fixtures, while Pirates must still face Durban City and Orbit College.
Galaxy, meanwhile, ended the evening in 12th place with 31 points from 29 games.
“I don’t think anyone else has played seven matches in 21 days, the calendar has beaten us and we need to recover as soon as possible,’ Cardoso told SuperSport after the game.
“We play a Champions League final in four days. FAR are on their third day of rest.”
Cardoso added: “I was going to tell them (the fans), if we had won today, that we would have scored a number of points that would have taken us to one of the three best campaigns ever at this club.
READ: TS Galaxy shock Sundowns to blow title race wide open for Pirates
“We would also have had the same points as the champions.
“We will see what will happen. But it was the calendar that beat us. We had 11 wins in a row since January. Then we played Esperance (Champions League semi-finals) and we drew twice in seven (Premiership) games and lost today.
“It is important for the fans to look honestly at the work of the boys. They can criticise the coach that is not a problem for me, I have big shoulders. I know the fans will be on our side this weekend,” said the head coach.
Sundowns play AS FAR in the Champions League final over two legs, starting on Sunday 17 May.