Champions Cup holders Bordeaux-Begles scored five tries in 18 first-half minutes as they swatted aside visiting Leicester 64-14 on Sunday to set up a showdown against French champions Toulouse in the last eight.
In Sunday's late game, eight-time finalists Leinster pulled away in the closing stages to beat Edinburgh 49-31.
In a deceptively even first 20 minutes, the hosts nosed ahead with a Maxime Lucu penalty, but after Cameron Woki breached the Leicester defence by reaching a long arm out to touch down from a ruck, the dam broke.
Louis Bielle-Biarrey, drew a crowd in the 25th minute before flipping a pass to Salesi Rayasi who trotted over untouched.
After Bielle-Biarrey had an acrobatic 31st-minute effort in the corner ruled out, Leicester kicked their drop-out back to him, and the Six Nations player of the tournament beat five defenders and drew two more before sending the unsupervised Lucu loping home.
Two minutes after that, Bielle-Biarrey, starting deep in his own half, accelerated. He crisply sidestepped five defenders and only one even laid a despairing finger on the flying winger on his sprint to the line.
"I was just happy to score," he said.
Another France star, Matthieu Jalibert, jinked through the Leicester defence after 38 minutes to send lock Maxime Lamothe lumbering over.
Izaia Perese replied for Leicester early in the second half but Ben Tameifuna immediately responded for the hosts. That try, like the first four, was converted by Lucu who then headed to the bench.
After Billy Searle again hit back for Leicester, Bordeaux replied with an eight-minute broadside of two tries by Rayasi either side of one by Arthur Retiere, all converted by Hugo Reus.
BLOCKBUSTER CLASH AWAITS
Bordeaux will host runaway Top 14 leaders Toulouse in the quarter-finals next Sunday.
"They're dominating the league outrageously, no matter which team they field," said Bordeaux prop Jefferson Poirot. "To be honest, watching them is hard to take because they're your potential future opponents."
Bordeaux won when the teams met in a Champions Cup semi-final last season but lost in the Top 14 final.
"Our paths are quite intertwined as we always come up against them in our group and in the knockout stages," said Lucu.
On Saturday, France centre Kalvin Gourgues scored two scintillating tries as Toulouse hammered Bristol 59-26.
"It doesn't matter who we face, we'll prepare the same way," said Gourgues about the prospect of another encounter with Bordeaux.
On Sunday, Leinster scored seven tries as they dominated Edinburgh in Dublin but set up four of the visitors' five touchdowns with interceptions or handling errors.
After Darcy Graham scooped up a loose ball and sped away to score after 51 minutes, the Scottish side led by two points.
But three tries in eight minutes, by Josh van der Flier, Tom Clarkson and Rieko Ioane wrapped up victory for the hosts who will host Sale next Sunday.
Sale's George Ford won the battle of the England flyhalves on Saturday, kicking 16 points against Marcus Smith's Harlequins in a 26-17 victory in west London.
Glasgow Warriors edged the Bulls 25-21 and will welcome Toulon next week after the French three-time winners held on while down two players to edge the Stormers 28-27.
England flier Henry Arundell also scored twice as 1998 champions Bath came from behind to see off English Prem rivals Saracens 31-22.
English champions Bath will face Henry Pollock's Northampton in the next round after last season's runners-up beat Castres 49-41 on Friday.