The sides were meeting for the second time in a fortnight, after leaders Province claimed a 41-17 win at Newlands just two rounds ago.
A much tighter affair was played out on this occasion, with Province holding a narrow 3-0 advantage at the end of a frantic first half.
Demetri Catrakilis stretched that lead with a penalty early in the second period, before the Bulls registered the first try of the match through Jacques du Plessis following good work by Jesse Kriel.
Tian Schoeman added three points from the tee to put the Bulls four points in front, but Kobus van Wyk went over in the corner just before the hour mark to snatch the lead back for Province.
Seabelo Senatla saw off three members of the Bulls' defensive line on his way to putting daylight between the sides.
After Schoeman and Kurt Coleman had exchanged penalties, Sampie Mastriet gave the Bulls hope by touching down in the closing stages, but the hosts were ultimately undone as a William Small-Smith knock-on brought an end to the match.
Golden Lions kept up the pressure on the leaders by posting a 41-22 win over Eastern Province Kings.
After edging the first half 21-19, the Lions stepped up a gear after the break to earn a bonus point.
In Saturday's remaining fixture, Free State Cheetahs triumphed 36-25 over Griquas, who - like the Kings - remain winless in this year's competition.
Friday saw Pumas pick up a 32-22 win over defending champions Natal Sharks to climb to third in the standings.
Pumas went over twice late on to seal a bonus point and protect their unblemished home record this season.