Cosmos made most of the early running with Bonginkosi Macala shooting high over Brian Baloyi’s crossbar from just outside the area in the fifth minute.
Sundowns imposed themselves on the game midway through the half and won a succession of corners, but failed to capitalise on their dominance.
Ezenkosi almost took the lead in the 41st minute, but Thapelo Tshilo’s fierce shot from the edge of the area flew straight at Baloyi.
A minute later, it was the visitors who threatened, with Lerato Chabangu shooting just wide from inside the area.
The match remained goalless at the break, with Cosmos looking the better side after the restart.
However, despite all their dominance in the opening stages, they failed to create any real clear-cut opportunities.
Sundowns almost broke the deadlock in the 64th minute, when Peter Ndlovu rose highest to meet Chabangu’s cross, but the striker’s header was comfortably saved by Avril Phali.
An inspired substitution by Trott Moloto saw Aldave replacing Ndlovu seconds from the end, with the match looking destined for a draw, but with seconds left, the Uruguayan ran onto a pass from Surprise Moriri to slot home from inside the area to hand Sundowns the points.