The victory was a welcome back gift for coach Jose Riveiro, who returned to the technical bench after serving a suspension during their previous match, which saw the Buccaneers lose 2-0 to Marumo Gallants.
With this win, Pirates remain in second place on the league standings, having accumulated 39 points from 17 matches.
Meanwhile, the loss for Chippa was a significant blow to their efforts to climb into the top half of the table. The Eastern Cape-based club sits in ninth place with 22 points from 19 games.
The match between the two teams was fairly balanced, with a few chances created at both ends, particularly in the first half. However, Pirates had the better of the opportunities and could have taken the lead as early as the 15th minute, but Kabelo Dlamini wasted a golden chance.
Chippa also looked threatening, especially with Giovanni Philander on the attack. The winger had a go at goal in the 22nd minute, but his attempted curler went wide, and he squandered another opportunity just two minutes later.
The best chance of the half fell to striker Tshegofatso Mabasa in the 38th minute, but his shot went straight to Chilli Boys goalkeeper Stanley Nwabali.
With the match seemingly heading into halftime at 0-0, Pirates' captain for the night, Sibisi, broke the deadlock with a well-taken header from a corner-kick to beat Nwabali at his near post, sending the Buccaneers into the break with a 1-0 lead.
With the home side chasing the game, coach Thabo September made changes, introducing fresh legs in attack by bringing on Eva Nga and Rondaldo Maarman to try and turn things around in the second half.
However, limited opportunities came their way, with Maarman's first shot of the match going straight to Pirates keeper Melusi Buthelezi, who was filling in for the suspended Sipho Chaine.
In the 78th minute, the Buccaneers thought they had scored their second goal of the match after substitute Goodman Mosele slotted in Mohau Nkota's cross. However, the referee ruled that the ball had gone out of play before the cross.
With just a few minutes left in the game, Chippa pushed for an equalizer, but the Pirates defence held firm until the final whistle, securing all three points for the visitors.