Sundowns had Malibongwe Khoza threatening a rampage with his second-minute goal before Tashreeq Matthews' first-half brace.
Sibanye then attempted to come back through goals from Mojafela Mokhatla, who beat disappointing Ronwen Williams with ease, and Boeletsang Rankali in the second half.
But Arthur Sales and Kobamelo Kodisang sealed victory for the Brazilians with goals that made life difficult for their stubborn opponents.
Sundowns' victory came as midfielder Bathusi Aubaaas was red-carded with 14 minutes to go for elbowing his opponent.