A late try from Wales scrum-half Mike Phillips gave Bayonne a 25-22 win over Newport Gwent Dragons in their Amlin Challenge Cup clash at the Stade Jean Dauger.
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But their failure to gain a try-scoring bonus point means Wasps can claim a place in the knockout stages with a five-point win over Italian minnows Mogliano on Saturday.
Phillips crossed with four minutes remaining after a try from Lewis Evans and 17 points from Tom Prydie looked like earning the Dragons an away win.
The visitors led 16-6 at the break thanks to Evans' 21st-minute score but tries from David Roumieu and Sam Gerber after 54 and 64 minutes had Bayonne back within a point at 19-18.
Prydie made it a 22-18 with a fifth penalty after 68 minutes but Phillips had the final say.