The result means that Bloemfontein Celtic are now the only team in the top flight not to have claimed a league victory this season, as they were beaten 1-0 by Kaizer Chiefs earlier in the day.
Both Pirates and Swallows seemed to have been given license to shoot on sight by their respective coaches, as the players let fly with efforts on goal from long range.
However, they rarely troubled goalkeepers Moeneeb Josephs and Greg Etafia, with perhaps the best effort being Cecil Oersen's drive in the 41st minute that forced the Buccaneers' goalkeeper into a parrying save.
Half time saw the two Soweto giants locked at 0-0, and one feels that both Ruud Krol and Julio Leal will have felt their teams could have performed better in the first 45 minutes.
The second half took on a similar form, though the Birds' Ramahlwe Mphahlele was unlucky to see his long range effort rebound off the upright in the 60th minute.
Krol reacted by sending on Lebogang Mokoena in place of the ineffectual Gilbert Mushangazike, hoping that the young forward would provide more mobility than the Zimbabwean.
The decision paid dividends as Mokoena played a key role in breaking the deadlock, setting up Mbuyane in 70th minute to beat Etafia and put the hosts 1-0 up.
Swallows sent on the duo of Shaun Haschick and Ryan Botha to try and bring their team back into the game, and the latter almost made an immediate impact with a free kick was punched to safety by Josephs.
Pirates looked to add to their lead on the counter as Swallows threw men forward in the dying stages; Dikgang Mabalane shooting wide just as the game headed into added time.