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Exeter remarkably clinched a place in the European Champions Cup quarter-finals after beating the Ospreys in bonus point fashion at Sandy Park.
The Chiefs ran in five tries - two each from wing James Short and number eight Thomas Waldrom, plus a Don Armand touchdown - to win 33-17 as Gareth Steenson added three conversions and Will Hooley one.
And with Bordeaux surprisingly beating Clermont Auvergne, it meant Exeter joined fellow English challengers Saracens, Leicester, Northampton and Wasps in the last eight.
The Ospreys, though, crashed out after scoring an early Hanno Dirksen try and claiming a late penalty try, while Dan Biggar kicked seven points, and Wales' wait for a top-flight European quarter-finalist - they last achieved it in 2012 - goes on.
But Exeter deserved all the plaudits after a stunning display that saw them finish top of the group against all odds.
The game began at a lightning pace in glorious conditions with three converted tries inside the opening 10 minutes.
Exeter made their intent clear when Steenson opted for a touch kick to the corner instead of attempting a long-range penalty, and after Waldrom made an initial charge, Armand pounced from close range.
Steenson's conversion made it 7-0, but the Ospreys quickly drew level following scrum-half Brendan Leonard's break, and before the Exeter defence could regroup, Dirksen crashed through a pile of bodies.
Biggar tied things up through an angled conversion, yet Exeter were immediately back into their stride, sparked by an arcing run from their Italy international centre Michele Campagnaro, before Waldrom finished things off and another Steenson conversion put the Chiefs 14-7 ahead.
The game inevitably settled down for a spell, but there was then a double injury concern for Ospreys as their skipper Alun-Wyn Jones left for a head injury assessment after being on the reciving end of a crunching collision, then Dirksen went off to be replaced by Sam Davies.
Jones quickly rejoined the action, but his second-row partner Lloyd Ashley departed after 29 minutes, limping out of the action and being replaced by Rory Thornton.
Exeter saw forwards Jack Yeandle and Geoff Parling go off for assessment after a 32nd-minute clash of heads, and Ospreys were content to soak up Exeter pressure as half-time approached.
Yeandle came back on just before the break, just in time to help his team close out the half and secure a seven-point interval lead.
With the wind at their backs, Ospreys began the second period in confident fashion, and a Biggar penalty from in front of Exeter's posts made it 14-10.
The Ospreys proved to be their own worst enemies just three minutes later, though, when Wales international hooker Scott Baldwin's reckless late challenge on Waldrom left referee Jerome Garces with little option other than to sin-bin him.
The look Baldwin received from his skipper Jones as he trudged off said everything and Ospreys were soon punished as Short ran straight through Davies' weak challenge, then outpaced Justin Tipuric for a try in the corner that put Exeter nine points clear and hotly pursuing a bonus point.
Short's second touchdown, which was sealed with another fine finish, looked to have sealed the deal, only for Ospreys to respond nine minutes from time when Garces awarded them a penalty try that Biggar converted after Exeter illegally halted a driven lineout.
But Waldrom had the final say, and when news of Bordeaux's victory filtered through to deepest Devon, the Chiefs' faithful embarked on wild celebrations.