Gilbert Mushangazhike, Teko Modise and Excellent Walaza scored for Pirates, in a game they dominated from the offset.
The Buccaneers created the first chance of the game in the eighth minute when Bennett Chenene saw his long range effort fly straight at Swallows keeper Greg Etafia.
However, Pirates went ahead five minutes later when Mushangazhike struck with a low shot from inside the area.
Swallows struggled to break down the Pirates defence, with their first real chance arriving in the 37th minute when Edzai Kasinauyo tested Senzo Meyiwa with a fierce long range effort, but the Pirates keeper was equal to the task.
Teko Modise almost doubled Pirates’ lead with a good free-kick in the 39th minute, but Etafia produced a superb save to tip the ball over the crossbar.
The score remained 1-0 at the break.
The Buccaneers continued in the same vein in the second half and doubled their lead in the 66th minute when Modise struck a superb goal from the edge of the area from a corner by Chenene.
Swallows rang the changes as they sought to get back into the game, but the Buccaneers extended their lead in the 85th minute when substitute Walaza scored from close range to seal the points for Orlando Pirates.