Pirates started brightly, as Ayanda Gcaba headed a right-wing cross from Mpho Makola against the crossbar as early as the second minute.
Soon after, Thamsanqa Sangweni drilled a free-kick narrowly wide from 30 yards out at the other end.
The Chilli Boys then took the lead in the seventh minute, as Zulu dispossessed Makola before going on a weaving run and beating Senzo Meyiwa with a clinical left-footed shot on the angle. It was the forward's fourth goal of the season.
The Buccaneers threatened twice before the half-hour mark, as Kermit Erasmus thumped a shot just over before marauding fullback Thabo Matlaba drew a save from Mbongeni Mzimela with a useful strike on target.
Makola also came close leading up to the recess, as he steered a free-kick just wide of the upright.
The second stanza failed to match expectations, as both sides struggled to make inroads in the final third.
Bucs, who lost the MTN8 Final last weekend, pressed in the latter stages, as substitute Lehlohonolo Majoro, on for Makola, turned sharply in the box before firing inches wide in the 75th minute.
Chippa nearly added a second at the death, but Meyiwa made a superb stop to foil a swift assault. Nevertheless, the hosts went on to claim the maximum spoils in Port Elizabeth.