Biarritz destroyed the Ospreys' hopes of European progress this season with a five-tries-to-one Heineken Cup drubbing.
The Welsh team arrived with hopes of a place in either the main competition's quarter-finals or the second-tier Amlin Challenge Cup last eight.
But Taku Ngwenya's hat-trick and tries by Benoit Baby and Iain Balshaw ensured defeat for the visitors.
Hooker Richard Hibbard scored the Opsreys' try in the second-half.
Biarritz remained in the hunt for a place in the latter stages of either European competition, their fate resting on games later in the day.
With number eight Imanol Harinordoquy and scrum-half Dimitri Yachvili directing their efforts, the hosts were able to control key parts of the opening period.
The visitors had few answers when the two French stars were probing and orchestrating the home side's efforts.
With Adam Jones anchoring their scrum, the Ospreys were able to largely dominate in that area.
And for Wales coach Warren Gatland, there were no further injury worries to add to those surrounding fly-half Rhys Priestland and flanker Dan Lydiate from the previous day's European action.
But that was of little consolation for being out-played in almost every other facet of play.
Yachvili was instrumental in giving Ngwenya the time and space to score the opening try after five minutes, the number nine adding the conversion.
The Ospreys had opted to give Eli Walker a chance in the number 11 jersey and put Shane Williams on the bench.
And there was a lesson for Walker to learn when he was caught out in defence by full-back Balshaw, who drew the defender before releasing Ngwenya for his second try in the opening 10 minutes.
Yachvili again converted and almost conjured a try for Harinordoquy with a clever cross-kick only for Dan Biggar to get his foot to the ball in time.
The home scrum-half added a penalty in the 25th minute and wing Williams entered the fray as full-back Barry Davies left it as half-time approached.
There were more replacements for the visitors at half-time, but scrum-half Kahn Fotuali'i lasted only five minutes before being sin-binned for a dangerous tackle.
In his absence the hosts found enough space to send wing Benoit Baby over and Balshaw was next to the line, also before Fotuali'i returned.
A rare line-out mix-up allowed Ospreys' replacement hooker Richard Hibbard to crash over from close range.
But Ngwenya completed his hat-trick as he left number eight Jonathan Thomas in his wake, Yachvili again converting.
Ospreys director of rugby Scott Johnson: "We knew it was going to be a hard day at the office because they started so well and us so poorly.
"When you have got that sort of tidal wave coming at you, it's hard to stop."
Biarritz captain Imanol Harinordoquy: "We played some of our best rugby of the season to win a European quarter-final.
"We're happy with the result because we knew the Ospreys are a strong team. They beat us narrowly in Swansea but this made up for that defeat."
Biarritz: Balshaw; Ngwenya, Gimenez, Traille, Baby; Peyrelongue, Yachvili; Barcella, Heguy, Marconnet, Thion, Carizza, Lauret, Guyot, Harinordoquy (capt).
Replacements: Haylett-Petty for Balshaw (66), Bosch for Gimenez (9), Bolakoro for Traille (62), Faure for Baby (72), Guinazu for Barcella (60), Terrain for Heguy (52), Gomez Kodela for Marconnet (48), Taele-Pvihi for Carizza (62).
Ospreys: B Davies; Bowe, Bishop, Beck, E Walker; Biggar, Webb; James, Bennett, A Jones, Gough, Evans, Smith, Tipuric (capt), J Thomas.
Replacements: Williams for B Davies (33), Morgan for Biggar (62), Fotuali'i for Webb (40), Bevington for James (40), Hibbard for Bennett (48), Bearman for Evans (64), R Jones for Smith (40).
Not Used: Jarvis.
Sin Bin: Fotuali'i (44).
Ref: Wayne Barnes (RFU).