Thulasizwe Mbuyane, Dikgang Mabalane and Gilbert Mushangazhike scored for Pirates, while Cecil Oerson and Elton Morelato pulled two goals back.
Pirates started brightly, scoring in the third minute thanks to Mbuyane, who headed the ball home after receiving a cross from Teko Modise on the left.
The Birds tried to get back into the game after conceding the early goal, but Pirates kept it tight in the middle of the park, thanks to some good work by Benson Mhlongo and Lebogang Mothibantwa.
Pirates scored their second goal in the 31st minute after Mbuyane put Mabalane through one-on-one with Swallows keeper Greg Etafia. The former Cosmos player neatly slotted the ball past the Nigerian minder, who injured his neck in his attempt to stop Mabalane and had to be replaced by Tyron Damons, making his debut for the Birds.
The best chance for Swallows arrived three minutes before half-time, but striker Phumelele Bhengu shot the ball over the top of the goal.
In a surprising move, Birds coach Leal replaced striker Bhengu with defender Fabian McCarthy at the start of the second half. Obviously, the Brazilian coach felt that in order to attack with purpose, he first had to re-organize Swallows’ defence.
Swallows tried to impose themselves in the second half, but it was Pirates who carved out the first chance of the second half when striker Mushangazhike found himself one-on-one with Birds keeper Damons, but the Zimbabwean failed to score.
But Pirates did get their third goal in the 61st minute. Modise delivered an excellent through-ball to Mabalane, who crossed from the right for Mushangazhike to finish from close range. The goal basically finished the game.
Still, Swallows managed to pull a goal back when Oerson’s powerfully hit free-kick from about swerved past Pirates keeper Moeneeb Josephs.
The former Bidvest Wits keeper even caused his Pirates coach a heart-attack when he completely misjudged a shot from outside the box by the Birds' Brazilian striker Morelato, sloppily putting the ball into his own net.
Some desperate defending by the Buccaneers in the dying minutes of the game, however, assured that Swallows ran out of time to score the equalizer. Mabalane was selected as the Man of the Match.
Moroka Swallows (4-4-2): Etafia (Damons 36); Kobola, Da Silva, Malinga, Mayinga; Oerson, Mazibuko (Morelato 63), Tsutsulupa, Botha; Radebe, Bhengu (McCarthy 46) Orlando Pirates (4-5-1): Josephs; Mahamutsa, Thwala, Seema, Mdledle; Mabalane, Mhlongo, Mothibantwa, Modise, Mbuyane (Mokoena 83); Mushangazhike