Making the victory even sweeter, it temporarily pushed the Capetonians into second place on the log with two matches remaining in the pool stages of the competition, although they will feel disappointed by the fact that they were unable to make the most of several other try-scoring opportunities throughout the match.
The first half was tight as both teams showed spurts of good attacking play, but a great try by Stormers centre Rikus Pretorius and two penalty goals and a conversion by Manie Libbok (flyhalf) to only one converted try by Glasgow Warriors No 8 Jack Dempsey saw them take a handy 13-7 lead going into the sheds.
The Stormers will rue missed opportunities in a second half in which they dominated on attack and created several opportunities to score, but they fought until the final whistle to score the bonus-point try compliments of hard-running No 8 Evan Roos.
The Capetonians had a few chances to put points on the board in the first quarter with an opportunity to kick a penalty goal and a few encouraging attacking chances, but they failed to capitalise on this.
Glasgow hit back with intent with some hard running on attack, and their efforts paid off with a try by Dempsey in the 18th minute from pick and go, and Ross Thompson (flyhalf) added the extra two to hand them a 7-0 lead.
The Stormers fought back hard despite making a few errors, with Libbok earning their first points in the 30th minute from a penalty goal, and Pretorius built on this with a stunning try minutes later from a well-timed change of direction on attack and a slick inside pass to the hard-running centre who dashed through to dot down.
They had another golden opportunity to score under the posts two minutes later after some fantastic team play and good running lines, but a knock-on denied them. Libbok, however, slotted a penalty goal soon after to nudge them into a 13-7 half-time lead.
The home side built on these 12 minutes into the second half as Springbok scrumhalf Herschel Jantjies received a pass from No 8 Hacjivah Dayimani who showed his pace and skill on attack before making the crucial offload.
Wing Leolin Zas added their third try almost immediately after, gathering the ball out wide and he stepped on the gas to make his way over the chalk. Libbok’s conversion saw them build up a 25-7 lead.
Stormers picked up the bonus point in the final minute
The Stormers dominated the second half creating one opportunity after the other, but mistakes at vital times combined with solid defence by the visitors denied them from adding to their score until the final minute.
Glasgow were dealt a big blow in the 68th minute after Josh McKay (wing) received a yellow card for a high tackle on Stormers centre Ruhan Nel, but they were unable to capitalise on this.
Roos, however, handed the hosts the breakthrough they needed to seal their bonus point as he crashed over from a hard dash on attack at pace in the final minute, which marked their fourth try of the game, sealing a rewarding 32-7 win for the team.
Tries: Rikus Pretorius, Herschel Jantjies, Leolin Zas, Evan Roos
Conversions: Manie Libbok (3)
Penalties: Libbok (2)
Try: Jack Dempsey
Conversion: Ross Thompson