Pitso Mosimane made only one change to the team that faced Chippa United at home in midweek with Thapelo Morena replacing Anele Ngcongca in the starting line-up.
The Brazilians were looking to extend their lead at the top of the league standings with a victory over a Baroka side which had drawn 0-0 with Platinum Stars away in midweek.
McDonald Makhubedu deployed Lucky Nguzana upfront as a lone striker just in front of Mpho Kgaswane, Rhulani Sidumo and Talent Chawapiwa.
Sundowns dominated the early stages of the game and Sibusiso Vilakazi fired the first shot on target, and he was easily denied by Baroka goalkeeper Ayanda Dlamini.
Baroka then suffered a blow as Talent Chawaphiwa sustained an injury and he was replaced by Robin Ngalande with the hosts forced into making an early change.
However, the hosts took a surprise lead when Lucky Nguzana turned the ball home following a well-played short corner to make it 1-0 to Baroka a few minutes before the half-hour mark.
The visitors piled pressure onto Bakgaka and they should have levelled matters through Gaston Sirino, who ran onto a well taken cross, but somehow he missed the target from close range.
Sundowns' pressure finally paid off just before the interval and it was Wayne Arendse, who equalized when he headed home at the far-post after a short corner to make it 1-1.
The two teams were locked at 1-1 at the interval.
Mosimane's men continued their dominace after the restart and they managed to take the lead for the first time through their star forward Percy Tau.
The South Africa international grabbed his 11th goal of the PSL season as he fired home from inside the box after a cut-back pass from Sibusiso Vilakazi.
Billiat and Tau were looking lively, and they combined well down the middle,before the former's shot on goal was easily saved by Baroka shot-stopper Dlamini.
Dlamini had come out to make save after Tebogo Langerman had set-up Billiat as Sundowns looked to extend their lead in the closing stages of the game.
Baroka launched late attacks in search of a late equalizer, but Sundowns stood firm at the back and they emerged 2-1 winners on the day.
The win sees the Brazilians extended their lead at the top of the league standings, while Bakgaga remained eighth on the table.