The result sees the Cape outfit climb back up to second in the URC standings, while the Bulls remain in eighth place.
The game started a good pace with both teams having tries chalked off by the TMO to set the tone for tight first half.
The Bulls took the lead when they were awarded a penalty try after the visitors had illegally stopped a maul close to the line.
Damian Willemse responded for the Stormers, running a brilliant to score a try unopposed.
Sasha Feinberg-Mngomezulu added the conversion and then another penalty as the Cape side took a slender 10-7 lead into the halftime break.
The Springbok flyhalf added a penalty eraly after the interval to extend the lead to six points.
Replacement flank Paul de Villiers then dotted as the visitors started to take full control of the contest with another penalty try given.
Bulls replacement scrumhalf Zak Burger scored five-pointer but it was mere consolation.
In a frantic closing, Willemse kicked in behind and Stormers replacement loose forward Hacjivah Dayimani raced through to score the bonus-point try.
Bulls coach Johan Ackermann admitted his side "fell apart" in their 32-19 home defeat to the Stormers at Loftus on Saturday, leaving his team facing a high-pressure run-in for the remainder of the United Rugby Championship season.
John Dobson described the Stormers' 32-19 victory over the Bulls at Loftus Versfeld on Saturday as "probably our most important win" and one of their most dominant performances in Pretoria since he took charge.
The Bulls have been forced into making a late change to their starting line-up ahead of Saturday's north-south derby against the Stormers at Loftus.
The Stormers welcome back three players with over 100 caps for the club in their United Rugby Championship derby against the Bulls at Loftus Versfeld on Saturday.
