The Buccaneers led at halftime through Thulasizwe Mbuyane and Takesure Chinyama, while Sifiso Myeni added another before Edward Manqele's late consolation.
Sundowns couldn’t afford anymore slip-ups in the League, and they got off to the better start when Teko Modise’s sixth-minute free-kick narrowly went just over the crossbar.
A moment of brilliance proved to be the difference in the opening stages when Mbuyane tapped home after good work by Chinyama.
It was a frustrating moment for Sundowns as they struggled to make anything from all their possession, with their own fans jeering Eleazar Rodgers for not being able to convert his chances.
And Pirates doubled their lead just before the break when they exposed the defence with some quick passing which eventually led to Myeni laying the ball off to Chinyama, who curled a 20-yard shot past Wayne Sandilands.
It was the same story just after the break when Daine Klate forced the goalie into a smart save, while Jabu Shongwe came closest for The Brazilians, hitting the crossbar with a powerful long-range drive.
However, Sundowns were out of ideas and eventually conceded a third when the former Bidvest Wits duo, Patrick Phungwayo and Myeni, interchanged passes before the latter finished with an expert finish.
Sundowns pulled one back through substitute Edward Manqele, but it was nothing more than a consolation, increasing the pressure on their coach Johan Neeskens.