The South Africans arrived in Scotland hoping to avenge their loss at this stage a year ago, but were met by a free-flowing Glasgow side happy to throw the ball around in sunny conditions - and the hosts were rewarded with tries from Rory Darge, Kyle Rowe (2), Henco Venter and George Horne.
Seabelo Senatla scored two for the visitors, but the uncharacteristic errors from their backline held them back as they struggled to hit their straps on Friday night.
Though the Stormers pack was their shining light, keeping their team in the hunt up to the hour mark with set-piece dominance, they were ultimately unable to prevent the Warriors from securing a place in the semi-finals where they will meet either Leinster or Scarlets in a week's time.
Quick start from the Stormers
It was a fast start from the Stormers, who were under the shadow of the hosts' sticks for much of the first five minutes before a knock-on ended the threat.
However, as they did for much of the game, the Stormers pack produced a huge scrum to win a penalty against the feed, giving Sacha Feinberg-Mngomezulu the simplest of kicks to make it 3-0.
But then came a period of momentum for the home side, who broke through Kyle Steyn to go right up to the Stormers' line. Senatla gave away a penalty for slowing the ball down at the breakdown, and was duly shown a yellow card for his efforts.
Having just lost captain Salmaan Moerat to an HIA, the Stormers were now rocked, and all the moreso when a deft lineout move from the Warriors saw Darge dive over for a simple score.
It then went from bad to worse for the 14-man Stormers as Sione Tuipulotu put in a perfectly weighted grubber for Rowe to gather and score a try which made it 14-3.
Feinberg-Mngomezulu added another penalty to somewhat reduce the arrears before the fly-half sent a free kick won by the Stormers pack into the swirling sky. None of the Warriors players put their name on the ball, allowing Senatla - only just back on the field - to canter over untouched following a kind bounce.
It meant the visitors were only a point behind, but lazy defending directly thereafter at a driving maul from close range saw Venter crash over on the blindside for a 19-13 half-time lead.
The Stormers threatened to make a game of it when a sweeping move down the left released Senatla for his second immediately after the break, but just as they had in the first half, Glasgow immediately wiped the score out with an effort of their own, this time through Rowe dancing around the defence near the line..
The hosts' cushion grew further when Horne scored a try which he converted himself, before slotting a penalty to make it 36-18 to the defending champions.
The game then calmed down into a more predictable rhythm as the Stormers were kept at arms length through solid Glasgow defence as well as their own poor handling, eventually ending their season in heartbreak at Scotstoun once again.