Goals from Eleazar Rodgers, Edward Manqele and Hlompho Kekana secured all three points for the Brazilians.
Mabhuti Khenyeza scored Ajax's only goal and then received a red card in the last minute for a second bookable offence as the Urban Warriors make it eight games without a win.
Ajax started brighter and looked to calm early nerves by grabbing a break through, with Khenyeza and Khama Billiat tring their luck inside the first 10 minutes.
But despite the visitor’s bright start it was the Brazilians who created the first real chance of the match, when Teko Modise played a good ball into the area. Wayne Arendse rose highest and directed a powerful header towards goal, but Sander Westerveld tipped the ball onto the post for a corner-kick.
Downs took the lead from the resulting corner, when Arendse directed Pelembe’s delivery into the path of Rodgers, and the striker made no mistake with his head from close range for only his second goal of the season.
Manqele doubled his side’s lead 10 minutes later, to take his tally to two in the League this season. Modise found the unmarked striker just outside the area and Manqele made no mistake, sliding a neat ball across the turf into the back of the net.
Khenyeza pulled one back for Ajax just before half-time, when his run at the near post was found by a great ball by Granwald Scott, and the ex-Sundowns striker slottED the ball neatly past Sandilands from close range.
Ajax started the second half as they did the first, looking to grab an early goal, but second half substitute Nyasha Mushekwi nearly made an immediate impact for the hosts, heading a corner by Pelembe straight at Westerveld, who was up to the task.
Kekana put the game beyond the Capetonians’ reach in second half stoppage time with his first goal of the season, netting from the penalty spot after he was brought down in the area.
Insult was added to injury when, in the final seconds of the match, Khenyeza was given his marching orders for a second bookable offence.
The wins means that Sundowns draw level with Univsersity of Pretoria in 10th place while Ajax remain in 15th, three points above Chippa United at the bottom.