Glasgow produced an almost super-human defensive effort to keep the French powerhouse at bay, while scoring on most of their rare visits into opposition territory.
The visitors led for 75 minutes thanks to some brave defending and a wonderful breakaway try from John Barclay.
Dan Parks slotted two penalties and a second half drop-goal but Damien Traille’s kicking kept the hosts in it.
But Biarritz cranked up the pressure in the closing stages and, following Justin Va’a’s sin-binning, Samiu Vahafolau crashed over for two late scores.
The French side move top of Pool 4, with Glasgow slipping back to third spot behind Saracens, who visit Viadana today.
Biarritz Tries: Vahafolau 2. Cons: Traille. Pens: Traille 3.
Glasgow: Tries: Barclay. Pens: Parks 2. Drop Goals: Parks.
BIARRITZ: Brusque, Ngwenya, Bidabe, Traille, Thiery, Peyrelongue, Cibray, Coetzee, Noirot, Avril, Thion, Dellape, Betsen, Harinordoquy, Cronje.
Replacements: Fa’afili for Bidabe (68), Willemse for Thiery (41), Bosch for Cibray (77), Balan for Coetzee (41), August for Noirot (41), Hall for Dellape (79), Vahafolau for Betsen (49).
GLASGOW: Stortoni, Faatau, Henderson, Gibson, O’Hare, Parks, Pinder, Va’a, Thomson, Low, Newman, Turner, Brown, Barclay, Beattie.
Replacements: Morrison for Gibson (75), O’Young for Pinder (41), Kalman for Va’a (41), Palepoi for Newman (70), Eddie for Brown (75).