Dean Ryan's team led for all but eight minutes of a thrilling European clash at Stade des Sports Aguilera yet still finished without a point.
Instead two tries each by Teddy Thomas and Yann Lesgourges saw the Basque club come from behind to win for the second time in a week while Benoit Baby's last-minute penalty denied Warriors a losing bonus-point.
It had looked a different story when scrum-half Su'a charged down a kick to score inside the opening minute.
Max Stelling and Paul Warwick followed in the second half, either side of a second yellow for Biarritz prop Thomas Synaeghel, while Ignacio Mieres also kicked 10 points.
But 14-man Biarritz stormed back with a late flurry to overtake Sale Sharks at the top of Pool 1.
Nicolas Sanchez scored 22 points as Newport Gwent Dragons missed the chance to go top of Pool Two, losing 32-13 at Bordeaux-Begles.
Bordeaux fly-half Sanchez scored an early try before Robert Lilomaieva and Jefferson Poirot crossed in the final 12 minutes.
But it was three yellow cards for Dragons forwards that proved just as decisive as the visitors' discipline deserted them at Stade Andre Moga.
Toby Faletau crossed before half-time to hand the Dragons a chance of victory but fellow forwards Andrew Coombs, Lewis Evans and Robertt Sidoli were all binned to leave the visitors facing an uphill struggle.
Dragons, who beat Bordeaux 40-22 last week, remain three points behind Bath who face Rugby Mogliano on Saturday and in the driving seat for a place in the last eight.
Brive beat Bucharest Wolves 20-9 but left the door open for Newcastle Falcons to take top spot in Pool Three after failing to collect a bonus point.
I Cavalieri Prato recovered from conceding an early try to beat Portuguese club Lusitanos to claim a second win in Pool Five.