Wasps trailed at half-time to Sam Gerber's second try of the tournament before Josh Bassett and Ed Jackson both crossed after the break to add to 16 points from the boot of Andy Goode.
Wasps next face Grenoble over the course of successive weeks and Dai Young will be well aware his side face a stern challenge after the French club kick-started their European campaign against Viadana.
Grenoble, who include former England fly-half Olly Barkley, have been one of the surprise packages of the Top 14 this season and still cannot be discounted in the pool despite lying third.
Jordan Michallet, Daniel Kilioni and Cedric Beal all scored two tries apiece in a remarkable match against Viadana that failed to produce a single point in the second half despite seven tries in the first period.
Bayonne remain second, thanks to their bonus-point win in round one and can keep the pressure on Wasps with successive games against the pool's bottom side, Viadana, in rounds three and four.