Exeter boss Rob Baxter was left to reflect on "an incredible finale" after his team secured an unlikely place in this season's European Champions Cup quarter-finals.
The Chiefs' 33-17 bonus point victory over Ospreys at Sandy Park saw them through on points difference after both teams and French challengers Bordeaux-Begles all finished level in Pool Two.
The three-way tie on 16 points was separated under tournament rules by results of games between the three clubs, with Exeter and Bordeaux, who were surprise 37-28 conquerors of Clermont Auvergne on Sunday, then still tied, which meant points difference being utilised and ultimately working in Chiefs' favour.
Exeter ran in five tries - two each from outstanding wing James Short and number eight Thomas Waldrom, plus a Don Armand touchdown - to triumph, with Gareth Steenson adding three conversions and Will Hooley one.
Debut Champions Cup quarter-finalists Exeter will be joined in the last eight by Saracens, Leicester, Racing 92, Wasps, Toulon, Stade Francais and Northampton.
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.
Baxter said: "I am obviously delighted, but delighted more for the players than anything else.
"Qualifying out of this pool today was very unlikely. Anyone who laid a bet on it has probably made a fortune!
"We talked about the character we wanted to show and what we wanted to take out of the game.
"We didn't expect to be winning the pool, but the players put in a fantastic shift and got a real tangible reward for it.
"We knew the score was staying pretty close between Clermont and Bordeaux, and it all started getting really confusing. We didn't know if we needed to kick the ball off the pitch at the end or score another try.
"It has been an incredible finale to the weekend. It is always nice when hard work gets rewarded, and I think that is what we have seen today."
Exeter will now visit Wasps at the last-eight stage in early April, and Baxter added: "We don't need to worry about Europe now.
"It's a long way away, and that is fantastic because it gives us a chance to thicken out our squad with players returning from injury. We will enjoy it tonight, and then it is back to business with the Aviva Premiership."
The Ospreys have now gone 20 successive away games in Europe without a win, and their latest setback will be all the more painful as they arrived in Devon knowing that victory would be enough to take them through.
"It was not the ideal start, conceding two quick tries. We brought ourselves back into contention, but the game got away from us and we gave ourselves too much to do," Ospreys skipper Alun-Wyn Jones said.
"First and foremost, we had to just come and win, which we didn't do.
"We are devastated, but you cannot live off emotion in this competition.
"We are still a proud bunch, and nobody said at the start of the competition that we would be in contention to get out of the pool.
"It is not about defying the odds and proving people wrong, it is about doing something different, but credit to the players to have come so close."