The Stormers faded late as the defending URC champions Glasgow Warriors claimed a 28-17 victory in Stellenbosch.
The Bulls, forced into late changes due to illness in the squad, left it late to claim a 17-15 victory over Benetton in the United Rugby Championship (URC) in Italy.
Flyhalf Kade Wolhuter has been included in Ivan van Rooyen's starting XV as the Lions travel to the Aviva Stadium to face Leinster in Round 6 of the United Rugby Championship.
Johan Grobbelaar is free to play after the Bulls' forward had his red card rescinded by a United Rugby Championship disciplinary hearing on Tuesday.
Director of Rugby John Dobson was thrilled with what was a crucial United Rugby Championship win for the Stormers against Munster at DHL Stadium.
It's a top-of-the-table clash when the United Rugby Champions only to undefeated teams - Lions and Leinster - go head to head on Saturday.