The Brazilians were desperate for a return to winning ways following their 2-0 to AmaZulu FC in the league earlier this week.
Thapelo Morena and Lyle Lakay returned to the starting line-up as Pitso Mosimane made two changes to the team that faced Usuthu at home.
Mimosas, on the other hand, were undefeated in their last two matches in all competitions having played to a 0-0 draw with AS Tanda in the Ivorian Premier League last weekend.
Mimosas coach Amani Yao Cesar named a strong starting line-up which included Ahmed Herve Diamonde, who netted in the team's previous Group A match against Lobi Stars.
The midfielder's solitary goal helped Mimosas beat Nigerian side Lobi 1-0 at home, while Themba Zwane's brace helped Sundowns beat Moroccan giants Wydad Casablanca 2-1 in the same week.
The Brazilians started the match brightly with Gaston Sirino looking lively as the hosts searched for an early goal to unsettle the visitors' defence.
Sundowns did grab an early goal and Sirino was involved as he whipped a good cross into the Mimosas box, and Mosa Lebusa headed home to make it 1-0 to hosts 10 minutes into the game.
It was not surprising that Sundowns broke the deadlock so early in the game as they went into the game having netted the majority of their goals (21.4%) in this period in the Champions League this season.
Lebusa turned a villain as he fouled Mimosas player Salif Bagate in the penalty area and the visitors were awarded a penalty.
Diamonde, who had netted from the spot-kick against Lobi, stepped up and beat Sundowns goalkeeper Denis Onyango to make it 1-1 in the 15th minute.
The hosts then piled the pressure on the Black and Yellows, and Lakay was unlucky not to score when his free-kick beat keeper Abdoul Cisse only for the woodwork to come to the visitors' rescue.
Mimosas then sat back and soaked up the pressure until Tunisian match referee Sadok Selmi blew for the half-time whistle with the two teams locked at 1-1.
Sundowns were the better side after the restart and they deservedly restored their lead following great team move involving Sirino and Zwane.
Sirino played a clever pass to Zwane, who made no mistake as he fired past Cisse to make it 2-1 to Sundowns nine minutes into the second period, much to the delight of the home crowd.
It was end-to-end stuff in the closing stages of the game with Cesar having introduced Burkina Faso attacker Ahmed Toure.
Sirino's shot was cleared off the line, while Lebusa rescued the Brazilians following a mistake by Onyango, who had failed to hold on to the ball.
Mosimane then introduced Emiliano Tade, who was making his official debut for Sundowns having joined the Tshwane giants from AmaZulu this week.
The Argentine striker made an immediate impact as he scored deep into stoppage time to seal a 3-1 victory for Sundowns after being set up by Zwane.
The victory saw the 2016 Champions League winners replace Wydad Casablanca at the top of the Group A standings, while Mimosas, who lifted the trophy in 1998, remained fourth.