Cardiff Blues withstood a second-half onslaught from Edinburgh to book their place in the Challenge Cup semifinals with a 20-6 win at Murrayfield.
Tries from Ellis Jenkins and Blaine Scully gave them a 14-3 half-time lead, while 10 points from the boot of Jarrod Evans helped edge them closer to victory.
Edinburgh's only points came from the boot of Jaco van der Walt as they failed to turn territory into tries.
Victory for the Blues capped a fine weekend for Welsh clubs in Europe following the Scarlets' Champions Cup win on Saturday, and their prize is a last four tie against Pau next month.
Gloucester survived a frantic finish to end Connacht's unbeaten run in the Challenge Cup with a 33-28 quarterfinal win at the Sportsground.
Replacement Billy Twelvetrees' 77th-minute penalty proved to be the final score of an eight-try thriller, as last year's runners-up set up a home semifinal against Aviva Premiership rivals Newcastle Falcons next month.
Tries from James Hanson, Tom Marshall and man-of-the-match Henry Trinder had the Cherry and Whites 17-10 up at half-time, with returning Grand Slam winners Kieran Marmion and Bundee Aki touching down for Connacht.
The hosts twice got back within two points thanks to second-half tries from Niyi Adeolokun and Matt Healy, but John Afoa's 55th-minute score on his 100th club appearance -- coupled with the place-kicking of Owen Williams (10 points) and Twelvetrees -- had Gloucester out of reach.
Newcastle's terrific season continued when they moved into the semifinals but Brive made them work hard for their 25-10 victory at Kingston Park.
It needed two second-half tries in the space of 10 minutes from winger Alex Tait -- both engineered by Toby Flood -- to break Brive's resistance and set up a semifinal away against Gloucester.
The hosts led 12-3 in the first half with tries from Scott Wilson Zach Kibirige before a brace from Alex Tait sent the 4,053 crowd home happy.
Pau hung on to beat holders Stade Francais 35-32 in a thrilling encounter to reach the semifinals.
Pau had looked to be cruising after establishing a 27-7 first-half lead, but their French rivals roared back and took the clash to the death at Stade du Hameau.
However, Stade could not find the one late score they needed and Pau survived to reach their first semi-final since 2005.
Jale Vatubua, Benson Stanley, Thibault Daubagna and Quentin Lespiaucq Brettes crossed for Pau's tries, with Clement Daguin, Charlie Francoz, Djibril Camara and Marvin O'Connor responding for the fallen champions.