The ultimate prize for the Frenchmen will be a first home draw in the knock-out stages, and they are well placed to finish in the top qualifiers.
The champions knew they faced an uphill task to come out on top in this seasons' 'Pool of Death' and only a bonus point victory would have been good enough to guarantee them a quarter-final slot.
That meant scoring four tries away from home against a team still high from their 21-17 victory at two time European champion's Leicester Tigers last weekend.
As hard as Wasps tried, not even a late from England prop Tim Payne, which clawed the scoreline back to 18-15 was good enough to save them.
And Wasps Lawrence Dallaglio believes the Frenchmen could go all the way this season.
"I always said the winner of this Pool would be good enough to get to the final of this competition," he said. "Whether they will then be good enough to beat one of the other big teams, we'll have to wait and see.
"Biarritz are worthy opponents, and anyone who can beat Leicester home and away and Wasps clearly has the quality to go on and win this competition.
"At this level, teams of Biarritz's size are going to put you under a lot of pressure, and their driving maul was a very effective weapon today."
Meanwhile Leicester's bonus point victory kept alive their slim hopes of taking the eighth and final qualifying as the second best runner-up on 19 points.
But that could all chance after Sunday's final round of Pool games, potentially leaving two former champions licking their wounds at the end of one of the most competitive Heineken Cup Pool stages on record.