The Buccaneers were 4-1 winners in the penalties with goalkeeper Sipho Chaine proving to the hero for the visitors before Tshegofatso Mabasa converted the final spot-kick.
Sundowns had looked in control of proceedings after taking the lead in the 17th minute when Iqraam Rayerns pounced on a rebound and buried his effort.
Rayners almost got his brace just after the halftime interval but the forward's low left-footed came back off the upright.
The Soweto giants were pressing for the equaliser and it almost came when Thalente Mbatha's long-range effort was headed into the net but Ronwen Willams leaped to make a brilliant save.
Pirates' relentlessness finally paid off and they made it 1-1 after 73 minutes when Kamogelo Sebelebele scored from a close-range after taking advantage of a scramble in the box following a cross by Oswin Appollis.
The game eventually went into the lottery of penalties with Chaine saving from Teboho Mokoena and Marcelo Allende before Mabasa delivered the knockout blow.
The Buccaneers will play either Sekhukhune United or Stellenbosch in the final.