Zakhele Lepasa marked his debut in the Soweto Derby with a goal, before Vincent Pule and Thembinkosi Lorch netted to inspire Bucs to their first win over Amakhosi since November 2018.
Coach Josef Zinnbauer made six changes to the team which took on Stellenbosch FC in midweek with Lorch making his return to the starting line-up.
However, Pirates' most capped player in the Soweto Derby, Happy Jele, was surprisingly dropped to the bench, while Thabang Monare made his debut for the Buccaneers.
On the other hand, Zinnbauer's counterpart, Gavin Hunt, who was taking charge of his first Soweto Derby match, made one change to the team which faced Chippa United in midweek.
Ramahlwe Mphahlele replaced Reeve Frosler in the right-back position, while 20-year-old sensation Nkosingiphile Ngcobo kept his place in the starting line-up after impressing against the Chilli Boys.
Chiefs were the better side in the opening exchanges with Khama Billiat causing havoc for the Pirates defence with his blistering pace and movement down the left-hand side.
The 30-year-old forward should have scored after beating two Bucs defenders, but his effort hit the crossbar from a one-on-one situation with goalkeeper Richard Ofori.
Billiat then got on his bike as he attacked the left channel, before setting up Leonardo Castro, who failed to hit the back of the net from close range as he placed his effort wide of the target.
Amakhosi were left rue those two big chances as Buccaneers broke the deadlock when Terrence Dzvukamanja's cross was headed home by Lepasa to make it 1-0 to Pirates in the 26th minute.
The visitors pushed for the equalizing goal, but an unmarked Siyabonga Ngezana failed to direct his header towards goal and the score was 1-0 to Pirates at the interval.
Amakhosi found it difficult to penetrate the Bucs backline in the opening stages of the second-half with Thulani Hlatshwayo looking solid at the heart of the hosts' defence.
Hunt reacted by introducing Bernard Parker and Happy Mashiane as the visitors looked to restore parity and get an important away goal.
However, Pirates continued to attack and they managed to double their lead when Lorch set up Pule, who turned inside the box, before scoring with a low shot to make it 2-0 to Pirates in the 67th minute.
Chiefs pushed forward in numbers as they looked to pull one back, but they were left vulnerable at the back and they were punished by Lorch following a quick counter-attack.
Second-half substitute Deon Hotto set up Lorch, who outpaced Mashiane, before firing past Chiefs keeper Daniel Akpeyi to seal Pirates' emphatic 3-0 victory in the 81st minute.
Pirates will take a 3-0 aggregate lead into the second-leg encounter which is set to take place at Chiefs' home ground, FNB Stadium on November 8.