Alje Schut scored with a diving header from Jabu Shongwe's cross on 91 minutes for the victory, though replays show at least three Brazilians being offside.
That means Kaizer Chiefs will need just a point from their remaining two games to clinch the League title; this after Platinum Stars lost to Golden Arrows.
Downs tried their luck early on from distance, with Tebogo Langerman having his shot blocked by Daine Klate, while Richard Henyekane fired wide.
Then, in the 22nd minute, Wayne Sandilands pulled off a great save to deny Khethokwakhe Masuku’s 30-yard screamer, parrying it around the post.
Pirates then started to gain momentum and were working some beautiful combination plays which resulted in Oupa Manyisa rattling the crossbar just four minutes later.
The Brazilians had to endure the same thing in the 41st minute when Wayne Arendse’s header off Elias Pelembe’s corner-kick hit the crossbar after he did well to rise above his marker.
Pirates had a chance straight after the restart when Collins Mbesuma worked his way into the box. The Zambian made a run to the byline but was fended off by Arendse, who forced the striker wide and he had to settle for a corner.
A large portion of the second half fell into a lull as both sets of players looked to have run out of steam and ideas to get the goal, though Manyisa came close when the ball fell to him near the end of the game, only for a defender to get in the way of his close-range shot.
A goal did eventually materialise though; Schut with a brilliant diving header back across goalkeeper Senzo Meyiwa, though replays suggested he was offside when the ball was swung in by Shongwe.
The defeat signalled a tenth consecutive League match without victory for Bucs, who remain seven points behind Amakhosi with only two matches remaining.
It also sees Sundowns move into the top eight for the first time this season.