Exeter produced their best performance of the season to beat Stormers and seal their place in the Heineken Champions Cup semi-finals.
Tom Wyatt crossed first before Jack Nowell and Olly Woodburn stretched the lead to 21-0 at Sandy Park.
Sam Simmonds added a fourth after the break to all but seal victory.
Damian Willemse, Suleiman Hartzenberg and Marvin Orie scored consolations for Stormers, while Jack Yeandle and Tom Cairns added the gloss for Exeter.
Chiefs will either travel to Bordeaux to face defending champions La Rochelle or play fellow Premiership side Saracens at Bristol's Ashton Gate in the semi-final.
With Toulouse knocking Sharks out earlier on Saturday, Stormers' defeat signals the end of South African involvement in this season's Champions Cup.
Exeter cruise through as Stormers crash out
Exeter qualified for the last eight in dramatic fashion, having scored more tries than Montpellier in their 33-33 result last weekend - a victory which looks to have kickstarted their season at just the right time.
Wyatt made his try-scoring European debut for the Chiefs against the French side, but the young full-back made it two tries in as many games after striding onto Joe Simmonds' pin-point crossfield kick to open the scoring.
If that try was the creativity, Nowell's score for the second was sheer power and guile as the captain drifted in off his wing to pick up from the base of a ruck, lunge through and pirouette around Stormers defenders to finish under the posts.
Woodburn, returning to the side after having to withdraw before the Montpellier game, was a constant threat and got the reward his endeavour deserved after a line-out move off the training paddock. The ball was thrown straight to Sean O'Brien at centre, who threw it back inside for Woodburn to pierce through and step the last defender for the third try.
The 2020 winners were comfortable and worthy of their 21-0 lead at the interval before Sam Simmonds spotted a gap in the Stormers defence to burst through and add a fourth, as the Sandy Park faithful began to make their plans for the next round at the end of the month.
Stormers' preparation for this game was not ideal, with delays meaning they did not arrive in the UK from Cape Town until Wednesday - so perhaps the United Rugby Championship champions' slow start was expected, but they improved after the break with the game seemingly beyond them.
Willemse dotted down after Seabelo Senatla freed his arms to offload before Hartzenberg latched onto Herschel Jantjies' clever box-kick for the second.
Ruhan Nel was denied a try on his 50th club appearance as Steven Kitshoff was adjudged to have blocked Henry Slade in the build-up, before Yeandle joined the back of the Exeter rolling maul after throwing the ball in for try number five.
Orie charged down Cairns' box-kick before beating the replacement scrum-half in the unlikeliest of foot races before Cairns hit back seconds later by finishing an Exeter move in broken field.
Exeter: Wyatt; Nowell (c), Slade, O'Brien, Woodburn; J Simmonds, Becconsall; Sio, Frost, Street, Gray, Jenkins, Kirsten, Tshiunza, S Simmonds.
Replacements: Yeandle, Abuladze, Iosefa-Scott, Davis, Ewers, Cairns, Skinner, Hogg.
Stormers: Willemse; Hartzenberg, Nel, Du Plessis, Seabelo; Libbok, Jantjies; Kitshoff (c), Dweba, Malherbe, Van Rhyn, Orie, Pokomela, Dixon, Theunissen.
Replacements: Kotze, Vermaak, Fouche, Porter, Engelbrecht, Dayimani, De Wet, Blommetjies.