Bucs reached their fourth final of the season via an own goal from Mario Booysen and stunning strike from Mpho Makola, with substitute Terrence Mandaza pulling one back for United at Harry Gwala Stadium.
The Premier Soccer League will on Monday announce the venue for the event decider, with Pirates drawn as the hosting side.
Earlier, Wits beat holders Kaizer Chiefs 4-2 on penalties after 120 minutes of football produced a 2-2 stalemate at Bidvest Stadium.
Pirates started their tie well, but Virgil Vries proved to be alert between the sticks as he stopped an effort from Makola in the opening minute before denying Daine Klate from close range in the 13th minute.
The Buccaneers continued to search for the opener and in the 20th minute it was Thabo Matlaba who used his skill to get rid of Michael Morton before shooting over the crossbar.
United had their first opportunity from a counter-attack four minutes later but substitute Mandaza, who replaced the injured Orlando Smeekes on 18 minutes, was unable to reach a low cross from Ruben Cloete.
Pirates had more opportunities before the break but they were unable to break the deadlock as Matlaba shot over the target in the 30th minute, while Oupa Manyisa fired straight at Vries three minutes later.
The opening goal came in the 52nd minute as Booysen deflected the ball into his own net after Kermit Erasmus’s shot was palmed onto the crossbar by Vries.
The visitors added a second on the hour-mark as Makola received a pass from Klate outside the box before beating Vries with a rasping low shot.
Manyisa had an opportunity to extend the lead in the 72nd minute after a free kick from Klate was pushed into his path by Vries but he ballooned his shot over the crossbar.
The hosts hit back a minute later as Mandaza fired home from the left side of the penalty area, connecting with a headed pass from Bongolwethu Jayiya.
The visitors were under pressure in the final minutes of the game as United pushed forward in search of an equaliser but Vladimir Vermezovic's men managed to hold firm.
Prior to Vermezovic's arrival in Mayfair, the Sea Robbers stumbled at the last hurdle of the CAF Champions League, the Telkom Knockout and the MTN8 under former boss Roger de Sa.