The game ended 1-1 at full-time, and Sundowns scored twice in extra time to take the game.
Isaac Chansa opened the scoring for Bucs with a penalty in the 8th minute.
Downs equalised through Koketso Mmotong on 83 minutes, and scored again three minutes into extra time through Lebohang Mokoena. Tso Vilakazi added a third on 115 minutes.
Pirates were down to 10 men after Josephy Kamwendo had received his second yellow card in the second half.
Ruud Krol's side started with a real sense of purpose and energy, which they maintained throughout the first half.
Sundowns coach Trott Moloto did not seem to have got his tactics quite right and his cause was not aided by some lacklustre play by Downs.
And it took Bucs just eight minutes to take the lead when Phenyo Mongala earned a penalty after he drew Esrom Nyandoro into a foul inside the box.
Isaac Chansa did the honours, beating the outstretched hands of Brian Baloyi with a spot kick into the right hand side of the net.
Pirates continued to dominate the game, looking far more hungry and they were close to a second when Mongala’s shot was deflected towards Mabena, but Baloyi made a brave save.
Mabena then missed a great chance when he was picked out by Mongala’s cross, his indecisiveness proving costly.
Sundowns had to wait until first half injury time for their first real chance, which saw Matthew Pattison bringing down a through ball expertly but then not having enough purchase on his right-footed shot which was saved by Senzo Meyiwa.
Pirates had two late chances in the half, but Mabena and Thulasizwe Mbuyane were not able to capitalise on a couple of goal-mouth scrambles.
Sundowns were given a lifeline to get back into a game in which they had been second best when Sea Robbers midfielder Joseph Kamwendo received his marching orders for second yellow card after 51 minutes.
This proved to be a pivotal moment as the complexion of the game changed dramatically after that.
Now it was the Brazilians who were on the front foot, pushing forward in wave after wave of attacks.
Bucs though did well to protect Meyiwa, but with the pressure remaining consistent from Sundowns, something had to give.
The breakthrough for the Tshwane side came in the 78th minute when Mmotong was left unmarked at the back post to slot home a straightforward first time shot.
Pirates though still had fight in them and it was the Soweto side who enjoyed the better of the chances in the remainder of regulation time as Dikgang Mabalane went close and Chansa had an 86th minute effort saved by Baloyi.
Sundowns appeared to be running out of steam towards the end of the 90 minutes, and the sides looked evenly matched.
But the Brazilians took the lead with a goal out of nothing when Mmotong’s snap shot struck the post, allowing Lebo Mokoena to slot home into an empty net from six yards out.
Pirates had to wait until the second period of extra time for the opportunity to level the game, but Chansa shot weakly while Mabalane’s cross glanced the bar.
But with Bucs throwing everything forward, gaps opened up at the back and Benedict Vilakazi added a third goal five minutes from time.