Joey Carbery’s 72nd-minute penalty, from all of 44 metres, decided this Pool 2 shootout in Munster’s favour as they advanced to a record 18th European Cup quarter-final.
Don Armand scored the game’s only try from a 12th-minute maul, giving Chiefs a 7-6 half-time lead in their pursuit of a result that would see them finish top of the table.
But Exeter could not edge out Munster and, in the end, Ireland fly-half Carbery knocked the Premiership leaders out with his third successful penalty of the night.
Despite claiming top spot in Pool 2 Munster will likely be away from home in the last eight, with the opposition probably Edinburgh, who won Pool 5. That will be confirmed this afternoon depending on Leinster’s result at Wasps.
In Pool 4 Ulster recovered from a 13-0 deficit to beat Leicester and claim a Champions Cup quarter-final place for the first time since 2014.
Dan McFarland’s side trailed 10-0 at half-time – and 13-0 soon after – but second-half tries from Marty Moore and Robert Baloucoune ensured they clinched a 14-13 victory at Welford Road to reach the final eight as one of three best-placed runners-up.
Racing 92 booked a home quarter-final with a 46-33 bonus-point victory over the Scarlets in Paris.
A brace of tries from Simon Zebo plus a try apiece from Juan Imhoff, Henry Chavancy, Virimi Vakatawa and Teddy Iribaren was enough to overcome a resilient Scarlets side. The Welsh region scored three tries of their own with Johnny McNicholl crossing twice and Steff Evans also touching down.