Jack Dempsey carried well in a powerful performance

Warriors led 6-0 at the break thanks to two penalties from the boot of player of the match George Horne edging them ahead, with Manie Libbok missing both of his attempts at goal.

Sebastian Cancelliere, Henco Venter and Ross Thompson crossed for second-half tries for Glasgow, Horne converting all three, to seal the 27-10 victory and book a place in the semi-finals where they will face defending champions Munster.

Ben Loader and Paul de Wet grabbed tries for the Stormers but Libbok's kicking woes didn't get any better as he missed both conversions.

Glasgow should have moved in front with the first real attacking move from either team. Their forwards stole the Stormers' line-out before the ball went through multiple pairs of hands until it reached Cancelliere on the opposite wing.

The Argentinian winger raced down the line and drew his man perfectly before passing inside to Horne who fumbled the pass, knocking the ball on right in front of the line.

Stormers were enjoying plenty of possession, too, and kicked for the posts after Zander Fagerson was penalised by the referee for using hands on the floor but Libbok pulled his effort wide of the posts.

The Warriors rarely kick for the posts but elected to take the three points on offer when Stormers were pinged, Horne atoning for his earlier error by making a straightforward kick.

There was a moment of concern for Kyle Steyn after the Glasgow captain caught Stormers full-back Warrick Gelant with his arm as the pair contested a high kick. The TMO and the referee consulted before deciding a penalty was sufficient punishment, with Libbok again failing to find the target from the tee.

When the home side were then awarded a scrum penalty, they again went for the posts rather than the corner, and Horne made no mistake in doubling his side's lead.

Stormers' cause was not helped when they lost their captain, Salmaan Moerat, to a yellow card in the second half after making head-on-head contact with Warriors' replacement Nathan McBeth. McBeth was helped off but was unable to return. Despite being a man down Stormers carried powerfully and were rewarded with the first try of the game.

Gelant fed Sacha Feinberg-Mngomezulu who offloaded to Ben Loader who went over in the corner. Libbok could not add the extras from out wide.

That temporarily stunned the home crowd, but it was not long before they had a score of their own to celebrate.

Stormers bobbled the kick-off, providing Sione Tuipulotu with possession, and his powerful run set up Cancelliere to score, with Horne converting.

The game had by now burst into life and Stormers gave themselves another lifeline when De Wet dummied and burst over from close range.

But Libbok again missed the conversion, from right in front of the posts, and Warriors' second try of the match settled the outcome.

Venter was the man to dive over after a series of pick-and-goes, before Thompson capped his 50th appearance and final Scotstoun appearance for Warriors by diving over right before the full-time hooter to complete the scoring.

After the match Glasgow Warriors head coach Franco Smith told BBC Scotland: "Really proud. We've talked all week about an 80-minute performance, applying ourselves the whole game to the best of our ability. There was some really intense commitment from the players tonight.

"The South African teams have added [physicality] to the competition and they can bully you physically, which makes it hard. That was one of the big work ons and the boys fronted up nicely.

"We smashed our windows of opportunity. I'm excited we converted those points and the way we controlled the game towards the end, from a discipline perspective, was very exciting.

"[George Horne] played really well tonight. We gave him a good platform to play from. He's a competitor, and I'm really proud of him. That's why we kept him on there for 80 minutes - to finish in the style he started.

"The less we think about what's happened [in the past], the better it will be. This is a new challenge, a different pitch to play on. They'll be waiting for us with a few plans, so this week we will come up with our strategy and take the game to them."