Goals from Anthony Laffor and Lebohang Mokoena helped the Pretoria side to a crucial 2-1 win over AmaTuks at Loftus Versfeld on Sunday
Laffor put Sundowns ahead in first half injury time, before Tuks drew level midway through the second period, courtesy of Atusaye Nyondo's header in the 63rd minute.
The Brazilians held their nerve and took the lead once more shortly after and held on for their fifth successive league victory, and sixth in all competitions.
Three points were enough for Pitso Mosimane to keep Chiefs on their toes, but trail the Soweto outfit due to an inferior goal-difference.
Sundowns bossed the opening exchanges and camped out in the Tuks half for much of the first quarter, as the visitors soaked up plenty of early pressure.
The hosts did not have it all their own way, however, as AmaTuks found their rhythm and got a few shots away at goal, none troubling goalkeeper Kennedy Mweene.
A frustrated Sundowns outfit were forced to bide their time and relied on a number of opportunistic attempts, including Surprise Moriri's audacious try from the halfway line, which forced goalkeeper Washington Arubi into tipping over a superb effort from the veteran.
At the other end, Atusaye's Nyondo had the best chance of the half as he curled a left-footed attempt goalwards, only for Mweene to make the game's best save, diving to his left and palming away well.
The Brazilians were eventually rewarded for their continued efforts as Laffor flicked on a delivery down the middle from Hlompho Kekana, beating Arubi with a crafty header on the stroke of half-time.
With a half-time lead secured, Sundowns came out into the second period looking to add another and nearly found it through skipper Alje Schut in the 57th, but the Dutchman glanced it narrowly wide.
AmaTuks soon put Sundowns to the sword after some lax defending, with Nyondo nodding home the equaliser from a throw-in deep into the Brazilians' half.
Mkhwanazi flicked on a neat ball after connecting with the throw in, leaving Nyondo unmarked and ready to pounce as he converted a simple finish.
The students' celebrations were short-lived though, as Sundowns regained the lead just three minutes after conceding, Mokoena glancing home a header from an acute angle to send the home side back in front.