Bayonne's Benjamin Boyet did most of the damage as his side beat Wasps in the battle of the unbeaten teams in Pool Three of the Challenge Cup.
Boyet kicked four penalties and converted Yoann Huget's first-half try to help them to victory.
The win was a boost for the French side who sacked their coaching staff and appointed former Japan coach Jean-Pierre Elissalde earlier this week.
Nick Robinson kicked two penalties but Charlie Davies's try came too late.
Bayonne: Heymans; Huget, Gerber, Mazars, Rokocoko; Boyet, Phillips; Manukula, Da Ros, Tialata, Linde, Flavell, Marmouyet, Puricelli, Baget.
Replacements: Lacroix for Huget (27), Boyoud for Tialata (56), Haare for Flavell (60), Lauaki for Manukula (63), Iguiniz for Baget (63), Roumieu for Marmouyet (67), Otazo for Boyet (71), Audy for Phillips (73).
Sin Bin: Da Ros (65).
Wasps: Southwell; Varndell, Waldouck, Flutey, Wade; N Robinson, Simpson; Payne, Lindsay, Broster, O'Donoghue, Wentzel, Jones, Everard, Hart.
Replacements: Burton for Hart (38), Castex for Payne (62), Taulafo for Broster (62), Daly for Varndell (66), Davies for Simpson (73).
Not Used: Morris, Harris, Davis.
Sin Bin: Flutey (30).