Stung by last weekend's defeat to Connacht Rugby, the Stormers responded emphatically, running in six tries to blow away the league leaders and take over at the top of the table.
The hosts set the tone early, with Sacha Feinberg-Mngomezulu slotting an early penalty before prop Ntuthuko Mchunu powered over for the opening try. Feinberg-Mngomezulu added the extras as the Stormers surged into a 10-0 lead.
Mchunu doubled his tally soon after, crashing over again as Glasgow struggled to contain the Stormers' forward dominance. The visitors' woes deepened when Jack Dempsey was sent to the sin bin, and Feinberg-Mngomezulu's boot stretched the lead to 17-0.
Glasgow briefly hit back through Ollie Smith, who sliced through the defence to score, but the Stormers quickly reasserted control when dlick interplay between Cobus Reinach and Feinberg-Mngomezulu sent Evan Roos over for a brilliant length-of-the-field try.
A late yellow card to Reinach allowed Glasgow to capitalise before halftime, with Gregor Hiddleston dotting down to reduce the deficit to 24-12 at the break.
Any hopes of a comeback were quickly extinguished after the restart. Feinberg-Mngomezulu extended the lead with a penalty before orchestrating a clinical attack to set up Ruhan Nel for the Stormers' fourth try.
Glasgow's discipline continued to falter when Adam Hastings was yellow-carded, and the Stormers took full advantage. Feinberg-Mngomezulu capped a superb individual performance by scoring himself after a dominant scrum, before adding the conversion.
The floodgates opened late on as Keketso Morabe forced his way over for the sixth try, with Feinberg-Mngomezulu maintaining his near-perfect record from the tee.