Clive Barker's men put up a brave display in front of an expectant crowd in Atteridgeville to extend their run to seven Premiership games without defeat.
Sundowns were on a similarly solid run of form and are now unbeaten in eight games in all competitions.
Sundowns enjoyed the lion's share of possession during the early exchanges and poked plenty of holes in Aces' defence.
Katlego Mashego, Surprise Moriri and Cuthbert Malajila all had early chances, but some good work from Jackson Mabokgwane kept his side in the contest in the opening quarter.
Aces hit back with a tame long-range effort after the half-hour mark, but Denis Onyango, who made his first appearance of the season, was up to the task.
Moriri came closest to breaking the deadlock late in the first half but his shot somehow went over the bar in what was the game's best chance up until that point.
Level at the break, Sundowns looked unsettled in the second half and struggled to create any meaningful chances.
That soon changed as Billiat and Tebogo Langerman had the AmaZayoni defence at sixes and sevens, but neither could test Mabokgwane.
That's how it would end as the two teams walked away a point in hand.