Linda Mntambo, Thamsanqa Gabuza and Abel Mabaso scored for the Buccaneers, who conceded a late goal at Amitie Stadium.
The Soweto giants advanced 8-2 on aggregate, having thumped the minnows 5-1 on home soil in the first leg of the preliminary-round tie.
Mntambo scored the opener 11 minutes in after combining with Zimbabwean playmaker Kudakwashe Mahachi, adding to the goal he scored in the previous meeting between the sides.
Striker Gabuza, who made his first start since his meltdown against Black Leopards earlier in the season, doubled the lead with his first goal of the campaign on the hour-mark.
New signing Mabaso added a third with his maiden goal for the club nine minutes later.
With the Telkom Knockout final in mind, Pirates coach Milutin Sredojevic picked virtually a new side compared to the one that drew 0-0 with Maritzburg United in the Absa Premiership at Orlando Stadium last weekend, with stand-in captain Mpho Makola the sole survivor.
Bucs next face Baroka in the TKO decider at Nelson Mandela Bay Stadium in Port Elizabeth on Saturday.
Pirates XI: Mabokgwane, Mabaso, Dube, Mobara, Da Silva, Makola, Mahachi, Mntambo, Qalinge, Gabuza, Mako.
Subs: Khuzwayo, Mbekile, Nyauza, Maphangule.