The win moves the Buccaneers to within two points of league leaders Mamelodi Sundowns with three matches remaining, while the defeat leaves Stellies rooted to 10th in the standings.
In front of a packed crowd, it was the Soweto giants who started the contest well with Oswin Appollis putting a left-footed effort wide from close-range.
Patrick Maswanganyi also fluffed a golden opportunity as the Buccaneers enjoyed a strong first half.
It took a two-goal blitz towards the end of the opening period, Evidence Makgopa and Maswanganyi finding the back of the net, that effectively sealed the contest.
Makgopa rose highest to head in Maswanganyi's cross from a free-kick that put the visitors ahead in the 42nd minute.
There was still time before the break for Pirates to get a second goal when Maswanganyi's cross beat everybody, including home goalkeeper Sage Stephens.
The clean sheet for Pirates also means shot-stopper Sipho Chaine has not conceded in 18 league matches this season, which is a record now shared with Bafana Bafana's Ronwen Williams.
Abdeslam Ouaddou's charges though will be happy enough to take maximum points and will no doubt be cheering on arch-rivals Kaizer Chiefs when they take on Sundowns at Loftus on Wednesday.
The Betway Premiership spotlight falls on Loftus Versfeld on Wednesday evening as Mamelodi Sundowns host Kaizer Chiefs in a clash that could be decisive in the title race.
Orbit College overcame Magesi 2-1 as Siwelele and Durban drew 2-2 in their Betway Premiership match on Tuesday evening.
Mamelodi Sundowns head coach Miguel Cardoso has scooped his third consecutive Betway Premiership Coach of the Month award.
Stellenbosch have announced a new partnership with historic sportswear brand Umbro.
