Andy Goode kicked 16 points as Wasps hit back from a 10-6 half-time deficit to earn victory in the Challenge Cup.
Sam Gerber gave Bayonne an early lead with a try which was converted by Stephen Brett before Goode missed with his first penalty of the night.
He was successful with three further efforts either side of the break before Ed Jackson put Wasps ahead with a try.
Josh Bassett scored Wasps' second try, after good work by Christian Wade, before Goode kicked another penalty.
It was Wasps' second straight victory in their group while Bayonne made it 11 games without victory against English sides.
England international James Haskell made his first appearance of the season when he came on as a 59th-minute replacement.
London Wasps: T. Bell; Wade, C. Bell, Hayter, Bassett; Goode, Simpson; Mullan, Festuccia, Cooper-Woolley, Cannon, Myall, Jackson, Thompson, Hughes.
Replacements: McIntyre for Mullan (63), Cochrane for Festuccia (58), Vea for Cooper-Woolley (59), Launchbury for Cannon (45), Haskell for Thompson (59). Not Used: Moates, Carlisle, Jacobs.
Bayonne: Spedding, Gerber, Fernandez, Ugalde, Fuster, Brett, Belie, van Rensburg, Roumieu, Muller, Fa'aoso, Chisholm, Monribot, Marmouyet, Fonua.
Replacements: Bernad for Belie (63), Arganese for van Rensburg (54), Iguiniz for Roumieu (54), Tialata for Muller (54), Rouet for Fa'aoso (63), Puricelli for Monribot (70), Boutaty for Marmouyet (65), Senekal for Fonua (70).
Sin bin: Bernad (76), Boutaty (78).
Ref: Peter Fitzgibbon (Ireland).