In the 18th minute Arrows scored when Sifiso Myeni lost possession to Arrows captain Thanduyise Khuboni.
Khuboni then proceeded to drive forward and played Nkosinathi Ogle through on goal, but he saw his initial shot saved by Moeneeb Josephs.
The Buccaneers keeper, however, failed to hold the ball and Bongi Ntuli pounced on the rebound to score the first league goal of the season and give his side the lead from a couple of yards out, 1-0.
Pirates suffered a further set-back in the 24th minute when Ndumiso Mabena had to leave the field injured, suffering a hamstring injury and was replaced by Thulasizwe Mbuyane.
Still, despite losing one of their attackers the Buccaneers continued to push forward in search of the equaliser, one they found in the dying seconds of the half.
Myeni delivered a quick in-swinging corner and Mbuyane met it with a powerful header from six-yards out to level matters before the break, 1-1.
The second 45 minutes saw Pirates come out a different side as the controlled the match from the restart.
But still, despite their dominance in the second half, they didn’t seem able to create any clear cut-chances on goal.
Instead the games third goal, which came in the 78th minute, was a spectacular long-range shot from another Pirates substitute.
A long ball forward was headed into Tlou Segolela’s path by Benni McCarthy, the substitute then let rip from 24-yards out and his shot almost burst the net as it found its way into the top left-had corner, 2-1.