Dai Young's side won their third successive tie to regain top spot in Pool Four, ahead of Bayonne, after taking maximum points at Stade Lesdiguieres.
There was little sign of the seven-try mauling to come when Joe Simpson missed with both his first two attempts at goal in the opening 10 minutes.
But Simpson's break and long pass handed Will Helu the opener after 13 minutes to fill Wasps with confidence.
Hayter's break saw Guy Thompson score his first try of the night to earn Wasps a 14-0 half-time lead
Centre Hayter crossed twice in the space of 13 minutes in the second half to firstly secure a bonus point and then kill off any lingering hopes of a Grenoble comeback. Thompson added his second try.
It was not until Hayter's long-range interception try that Wasps could finally relax after Grenoble mounted a fierce comeback sparked by Cedric Beal's try, converted by Olly Barkley.
Jack Winter-Moates stepped off the bench to finish a break by Tom Lindsay in style six minutes from time before Josh Bassett completed the rout.