Biarritz (3) 21
Barclay was one of several outstanding performers for Glasgow
Tries: Vahafolau 2
Pens: Traille 3
Glasgow (11) 14
Pens: Parks 2
Battling Glasgow were denied a Heineken Cup double over Biarritz after conceding two late tries.
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.
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 on Saturday.
Glasgow could not have dreamed of a more inspiring start as they opened up an 11-point lead in the first quarter.
Parks took advantage of some sloppy play from the over-anxious home side to slot over two penalties.
Even better was to come for the Warriors when Barclay burst clear of a crowd of markers and beat American winger Takudzwa Ngwenya in a race from 35 metres.
Tenacious tackling and clever marshalling by the Glasgow defence staved off a reply, but they were powerless to stop Traille getting his team off the mark nine minutes before the break with a simple penalty.
Traille added two more strikes, with Parks slotting an opportunist drop-goal in between.
With the clock ticking down and the home side pouring forward, Va'a, who had re-entered the action, was yellow-carded for lashing out in retaliation.
Biarritz spurned the chance of three points and instead went for position in the corner in their bid for a try.
And their enterprise paid off as substitute Vahafolau plunged over for the score, goaled by Traille.
Vahafolau completed his last-gasp double after a Parks drop-goal attempt was blocked.
Glasgow head coach Sean Lineen:
"I'm exceptionally proud of a bunch of guys who gave everything.
"They can hold their heads up very high after what was an outstanding defensive display.
"We put up one hell of a fight and we're not dead in this group yet."
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). Not Used: Milligan, Barrow.
Sin Bin: Va'a (76).