The Buccaneers claimed maximum points despite facing a late push from their rivals, who were forced to finish the encounter with 10 players after Inacio Miguel received a red card in the dying moments of the match.
The victory sees Pirates leapfrog Mamelodi Sundowns to the top of the standings with 25 points, two ahead of second placed Brazilians, while Chiefs remain fifth with 14 points.
It was an entertaining encounter, with both teams creating several opportunities in a game that could have produced more goals.
Chiefs enjoyed a brighter start, with Wandile Duba and Pule Mmodi causing problems for the Pirates defence. Duba came particularly close to opening the scoring but directed his effort straight at goalkeeper Sipho Chaine.
Mfundo Vilakazi and Mduduzi Shabalala also looked lively as Amakhosi continued to put pressure on their opponents.
However, Pirates gradually found their rhythm and took the lead in the 24th minute. Yanela Mbuthuma's effort took a deflection off a Chiefs defender before finding the back of the net, leaving Brandon Petersen with little chance.
Amakhosi responded positively and restored parity just six minutes later. Chaine failed to hold onto the ball, allowing Mmodi to capitalise and make it 1-1.
Chiefs finished the first half strongly, with Vilakazi and Shabalala continuing to trouble the Buccaneers' defence.
The second half saw both sides searching for a decisive goal, but it was Pirates who found the breakthrough in the 55th minute.
Thapelo Mokobodi made a good run through the Chiefs defence before picking out Tshepang Moremi, who calmly finished to put the visitors 2-1 ahead.
Amakhosi pushed forward in search of another equaliser, with Duba once again denied by Chaine in the 68th minute.
Pirates came close to extending their advantage in the closing stages when Moremi struck the woodwork in the 84th minute, before substitute Oswin Appollis had a goal ruled out for offside.
Chiefs' hopes of rescuing a point suffered another setback in stoppage time when Miguel received a second yellow card for a foul on Gamphani Lungu.
The defender's dismissal left Amakhosi with 10 men as Pirates held on to secure a memorable derby victory, three valuable points and top spot in the league.
AmaZulu recorded a fifth consecutive victory in the Betway Premiership after defeating KZN rivals Golden Arrows while Chippa United and Kruger United also picked up wins on Saturday.
Mamelodi Sundowns returned to the top of the Betway Premiership standings after thrashing Durban City 4-1, with Thabang Matuludi scoring twice at Loftus Versfeld on Saturday.
Football agent Mike Makaab believes that scoring goals consistently does not automatically guarantee a striker a move to a bigger club, insisting that several factors influence transfer negotiations.
AmaZulu coach Arthur Zwane wants another statement performance from his side when they face KwaZulu-Natal rivals Golden Arrows in the Betway Premiership derby at Moses Mabhida Stadium on Saturday.
