Defending champions Exeter Chiefs had to come from behind to beat Lyon 47-25 in the last 16 of the European Champions Cup on Saturday while Kotaro Matsushima's last- gasp try sent Clermont into the last eight.
The Japan full-back wriggled over the line with the last play of the game as Clermont edged Wasps 27-25.
Their reward will be a home quarter-final meeting with fellow French side Toulouse, after Antoine Dupont's late double-strike saw the four-time champions past Munster 40-33 at Thomond Park.
The two French victories made up in part for the elimination of Toulon on Friday after their match against Leinster in Dublin was cancelled because of a Covid-19 case in the visitors' squad.
Exeter, who will now face Leinster, produced a fairytale end to 2020 when they beat Racing 92 in the final in October.
However, they were in nightmare territory as they shipped two early tries from Baptiste Couilloud and Xavier Mignot to trail Lyon 14-0 after eight minutes.
Stung into action, Chiefs hit back with two tries in quick succession from Scotland's Jonny Hill.
Tom O'Flaherty and Ollie Devoto added further scores to give the champions a 26-20 lead at half-time.
Exeter took control of the game in the second half and further tries from Dave Ewers, Olly Woodburn and a penalty try completed a convincing.
- Matsushima magic -
Clermont trailed by five points at Wasps with barely 20 seconds left on the clock when they were awarded a penalty which they kicked for a lineout on the English side's 22 metre line.
After Clermont's forwards and bigger backs spent three minutes battering their way towards the Wasps line, Matsushima found a gap and, although tackled short of the line, squirmed over to level the scores.
Camille Lopez converted with the last kick of the game to send Clermont into the quarter-finals.
"I thought the boys showed massive character in the last 10 minutes," said Clermont No. 8 Fritz Lee.
Clermont have reached the final of the competition three times but lost each time.
"As a club, as a personal dream, we're always trying to chase down that European Cup," said Lee.
Winger Paolo Odogwu dotted down for Wasps after just six minutes and two minutes later, fullback Matteo Minozzi created the opportunity to score again.
The Italian completed a passage of individual brilliance by dropping the ball as he opted for a spectacular dive over the tryline -- it was to prove a costly mistake.
Scrum-half Sebastien Bezy cantered over for Clermont in the corner and visitors took the lead when prop Peni Ravai crashed over from close range.
Josh Bassett and Ben Harris both touched down as Wasps opened up a 25-20 lead but it was not enough to hold off Matsushima's last gasp heroics.
- Dupont double -
Ireland wing Keith Earls gave Munster the perfect start against Toulouse, going over for two superbly taken tries within the space of three minutes, midway through the first half.
Three penalties from Romain Ntamack meant Toulouse only trailed 16-9 at the break and they moved level shortly after the restart when Ntamack chipped over the defence for wing Mathis Lebel to leap, catch, dive and finish all in one fluid movement.
After that, momentum swung back and forth.
"It was a bit of a ping-pong match for the rest of that second half," said Toulouse No. 8 Jerome Kaino.
Munster flanker Damian Coombes and Toulouse hooker Julian Marchand both rumbled over to keep the two giants toe-to-toe at 23-23.
JJ Hanrahan nudged Munster ahead with a penalty with 13 minutes remaining but Toulouse against responded in style as Lebel left Hanrahan clutching at thin air before feeding scum-half Antoine Dupont who went through for the try.
Ntamack added the conversion to make it 30-26 and added a penalty when James Cronin was penalised at a ruck.
Two minutes from time France scrum-half Dupont assured Toulouse's place in the last eight with his second try of the game.
Munster had the final say when Coombes also went over for his double but Toulouse marched on.