Lehlohonolo Majoro struck twice to go with goals from Siyabonga Sangweni and Kermit Erasmus as Bucs ended a four-game winless run in the Absa Premiership.
The Sea Robbers, though, will be sweating over the fitness of striker Lennox Bacela, who was forced off with a knee injury before the break at Orlando Stadium.
Pirates dominated a goalless opening half, but Bacela and Majoro were unable to beat the perfectly-placed Anssi Jaakkola with low shots on target.
The Buccaneers then lost the services of Bacela in the 57th minute after he collided heavily with former Bafana Bafana midfielder Lance Davids, prompting the introduction of fellow forward Erasmus.
Eric Tinkler's men, however, took control of the tie with three unanswered goals in an eight-minute spell.
Majoro got the opener as he steered in a 58th minute corner, with the ball hitting the woodwork before bouncing in off the back of Jaakkola.
The ex-Kaizer Chiefs man completed his brace three minutes later with a tap-in on the rebound after Jaakkola kept out an effort from Erasmus.
Sangweni also got in on the act in the 66th minute when he was allowed to slot in a corner unchallenged in the Ajax box.
Erasmus was likewise not to be denied, as he sealed the rout with a composed finish in the final minute.