Cuthbert Malajila gave Sundowns the lead just before half-time with a brilliant, looping header from Hlompho Kekana's free-kick.
The game looked to be turning when Mzikayise Mashaba was shown a red card for a second bookable offence in the 63rd minute following a late challenge on Stars goalkeeper Johnny Mathole, who produced several good saves throughout the match to keep the scoreline down.
But Khama Billliat gave the Brazilians a two-goal cushion with a fine, left-footed strike from the edge of the area into the bottom-right corner after neat work from substitute Themba Zwane.
Billiat then missed two more chances to make the game safe but showed poor decision-making in the final third as Sundowns continued to create chances despite being a man down.
It was a much better second-half performance from the Brazilians, who did not find their usual rhythm in the first half but showed great tenacity in the second half, as left-half Tebogo Langerman's tracking back and last-ditch tackle to preserve the clean sheet showed.