Stormers arrived at Scotstoun sitting top of the URC table but Warriors made the most of a first half purple patch that saw them go over for three tries.
Man-of-the-match Sione Tuipulotu went over for the first after clever interplay and decoy work from the Glasgow backs first try before Johnny Matthews added to his impressive try-scoring stats with two more. Stormers will surely be there or thereabouts come the end of the season so Glasgow's win was impressive enough, but there was slight frustration as the bonus point remained elusive during a second half that yielded no points.
"I think yeah maybe," Glasgow wing Sebastian Cancelliere told The Scotsman after being asked if there was slight disappointment over the bonus point. "There were maybe lost opportunities that we created but didn't score. That for me hurts a little bit. But you have to respect as well the other team. Stormers is a great opposition who won their first two games. So we knew it was going to be a physical battle. We prepared for that and the forwards did a great job.
"It wasn't very pretty but every time they scored we replied instantly. There was a good reaction to the two times they kicked for the posts, right away from the kick-off we scored. That was a massive thing for us. And in defence there were one or two plays where they kept going and going and then there would be a turnover for us. Those were key moments when we were under stress. The forwards, especially, but all the team stepped up and that was a massive thing."
A continuation of Glasgow's impressive home record will be vital to their ambitions for the new season. Last season Franco Smith's men went unbeaten at Scotstoun in the regular URC campaign before losing to Munster in the play-offs.
Cancelliere recognises the importance of Glasgow's home form, but he's determined to improve their fortunes away from home - starting with next Saturday's visit to Wales to play Ospreys.
"Scotstoun is always a special place for us but the big thing for us now is to win more on the road," said Cancelliere, who became a father for the first time last week. "To be a great team you have to win consistently, not only at home but also away. We want to be one of the best teams in the competition and for that you need to win away. That's our mindset. Next week we have a good game to try to prove that against Ospreys."