All their points came in the first half when they were down to 14 men with hooker Deon Fourie sent to the sin bin for an off-the-ball shoulder charge.
Tries from Damian de Allende and Nizaam Carr in a five-minute spell brought relief to the under-fire Stormers coaching staff as their team grabbed only a second win in eight games this season.
De Allende's try was the result of quick thinking from captain Jean de Villiers, who took a quick tap penalty to set up his fellow centre, while Carr stormed through three tackles to make his score.