The Soweto giants found their opener only seven minutes into the clash as they made the most of a set-piece. Monnapule Saleng floated it for Thabang Monare to head home.
A big mistake from Sage Stephens then cost Stellies dearly as Bucs skipper Innocent Maela shot into an empty net for a 2-0 advantage.
Stellies were able to stop the bleeding to recover during the half-time interval, but the second half went the way of Pirates as well.
Just shy of the hour mark the hosts scored their third as Kermit Erasmus joined the party as he steered Saleng's cross into the back of the net.
Phillip Ndlondlo capped off the impressive performance with a stunning long-range shot.
Stellies managed to score a consolation goal in the 74th minute when Mervin Boji provided the visitors with a finish.
The victory puts the Soweto side in fourth position in the standings, with SuperSport two points clear in third, while Richards Bay are two further points ahead in second. Sundowns have a 17-point lead over second.