Munster came through a thunderous test of their Heineken Champions Cup credentials as they ended Exeter's hopes with a 9-7 defeat in front of a capacity Thomond Park crowd.
Joey Carbery's 72nd-minute penalty, from all of 44 metres, decided this Pool Two 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.
While the defence-dominated phases meant there was no chance of pressing for four tries, Exeter could not edge Munster out of losing bonus-point range either and, in the end, Ireland fly-half Carbery knocked the Gallagher Premiership leaders out with his third successful penalty of the night.
Despite claiming top spot in the pool and maintaining their excellent home record against English opposition in Europe, Munster will be away from home in the last eight.
The opposition is likely to be Guinness PRO14 rivals Edinburgh, who won Pool Five. That will be confirmed on Sunday afternoon depending on Leinster's result at Wasps.
Absorbing a typically abrasive start from Chiefs, Munster were first on the board with Carbery, their man-of-the-match against Gloucester last week, punishing a maul infringement from Jonny Hill in the sixth minute.
However, Exeter had the lion's share of possession in the first half, with Nic White, Don Armand and Dave Dennis particularly influential.
They were deadly accurate from their first maul opportunity in the Munster 22, the hosts bringing down the drive illegally before flanker Armand managed to barge over with Alex Hepburn in support.
Joe Simmonds converted for a 7-3 lead, both teams drawing breath after a frantic opening quarter of an hour.
Carbery doubled his tally with a well-struck 22nd-minute penalty, rewarding an advancing Munster scrum, but the high stakes made for a scrappy contest dominated by tactical kicking.
Exeter over-complicated their next lineout chance and handed back possession, as they did a few minutes later when Tadhg Beirne won a relieving penalty for Munster at the breakdown.
A brief dust-up after Henry Slade was bundled into touch raised the tension and decibel level.
Worryingly for the home fans, poor game management from Munster almost saw them concede past the 40-minute mark. Instead, Mike Haley dived on a spill by Tom O'Flaherty and the one-point margin remained in place.
The third quarter was effectively a stalemate with neither side able to make a breakthrough. Munster were guilty of some loose kicking, giving Jack Nowell opportunities to counter past halfway, and Exeter, who continued to have the better of the breakdown battle, carried the more consistent threat with ball in hand.
An Andrew Conway kick-chase finally opened up the Exeter defence in the 60th minute, only for Conor Murray to take the wrong option from a turnover as he was crowded out in the right corner.
Winger Conway pressed again from a chip-kick soon after, but ever-influential Australian White showed his class with a terrific touchfinder that moved the visitors back into try-scoring range.
Although Rob Baxter's charges sensed a try after Peter O'Mahony coughed up a lineout penalty, Billy Holland made an immediate impact off the Munster bench with a crucial steal at the set-piece.
Suddenly it was Munster who were winning the collisions. A Sam Skinner lineout offence allowed Carbery to coolly reclaim the lead for the Irish province, whose re-energised defence was summed up by a game-ending double tackle by Keith Earls and O'Mahony, at the end of 22 phases from Chiefs.
