Pirated dominated the majority of possession and had several shots off target, although Chippa also looked threatening when they did have the ball.
Issa Sarr had the ball in the back of the net in the 15th minute but the goal was disallowed as the midfielder had gained an advantage by being in an offside position before tapping in Sifiso Myeni's excellent cross.
Sarr was not offside when the final ball was played by Myeni but had been in an offside position prior to Myeni's brilliant dribble into the box and was already behind the last defenders, meaning he gained an advantage from his initial position.
Ayanda Gcaba had to be alert to intercept just as Mark Mayambela was being played through for a one-on-one in the area, while Philani Shange also had a shot go wide midway through the half.
Bucs had a few shots from outside the box but both Luvuyo Memela and Oupa Manyisa narrowly missed the target, while Chilli Boys goalkeeper Daylan Hawes only had a tame Memela shot and weak Thamsanqa Gabuza header to save.
Then Pirates got the breakthrough they deserved early in the second half as an unmarked Gcaba headed in Myeni's corner-kick at the far post, just minutes after Siyabonga Sangweni had a goal ruled our for another offside and Gabuza had missed a sitter of a near-post diving header from Erasmus' right-wing cross.
Chippa suffered a huge blow in the 66th minute when referee Victor Gomes showed a second yellow card to Ugonna Uzochukwu for leading with his elbow on Gabuza, with the Nigerian stunned at the decision. Replays suggest the player was very unlucky, but off he marched.
Eric Tinkler's men threatened to make things difficult for themselves when Buyani Sali pulled one back after a swift, one-touch-passing move from Chippa as substitute Mhlehgi Cele played the final ball to Sali to slot into the bottom-right corner.
Chippa had a spell of pressure on the Pirates goal as Siyabonga Mpontshane was forced to save from Mayambela before being caught in no-man's-land from the resultant corner as the ball flashed across an open goal.
But Pirates turned on the style and made their one-man advantage count towards the end of the game as the Chippa legs tired, with substitute Mpho Makola producing two stunning strikes from range right after an apparent own-goal by Chippa keeper Hawes.
Depsite the goal being credited to Erasmus, Hawes appeared to get the last touch after Gabuza's flick-on was headed on target by Erasmus, who applied enough pressure on the rebound save to force Nkosinathi Mthiyane and Hawes to get in each others' way and put the ball in their own net.