Sundowns came into the game with consecutive defeats, but got off to a lively start when Sibusiso Vilakazi nearly got them in front in the opening minute.
Buoyed by a fervent home crowd, Ajax did not retreat but posed problems of their own, particularly with their pace.
Fagrie Lakay got the game’s first shot on target after 12 minutes when he beat the offside trap only to see his effort dealt with by Denis Onyango.
Downs were battling to get an offensive grip on the game, and at best were reduced to shots from range that were of no problem to Brandon Petersen.
Consequently, they went behind when Lakay shrugged off Thapelo Morena’s challenge before slotting the ball into the bottom corner in the 27th minute.
The goal shook the visitors, and in succession Petersen stood up to deny Oupa Manyisa and Percy Tau from levelling matters before Motjeka Madisha saw his header going agonisingly wide of goal earlier on.
Petersen could do nothing though to prevent Ricardo Nascimento equalising from the spot after Isaac Nhlapo was adjudged to have handled inside the box.
Vilakazi, who had been guilty of glaring misses previously, found his first goal of the season two minutes later with an easy tap-in following Tau’s delivery.
A minute after the break, the Urban Warriors nearly drew level, but Lakay blasted over the bar with the goal at his mercy.
Muhsin Ertugral rang the changes in search of the equaliser, but they failed to master any meaningful attack.
In contrast, the Brazilians continued with their patient build-up game and troubled the hosts on a few occasions.
With time running out, Sundowns were in complete ascendancy as they spread passes with consummate ease, with the Urban Warriors offering little in response.
It proved to be sufficient for Pitso Mosimane’s side to return to winning ways and stretch their lead at the top of the standings to four points ahead of second-placed Cape Town City.