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The home side went further ahead just a minute later as Ruaridh Jackson chipped the ball over the Toulon defence, Joe Simpson picked it up and played it to Joe Launchbury, who found Jackson again to race clear for Wasps' second try.
Pelissie put up three points for the French side after a penalty from a power scrum, but Elliot Day hit a kick from halfway to extend their lead back to 14 points.
Day could have put his side further ahead but missed his kick before Jackson added another penalty with 10 minutes of the first half remaining, although Pelissie was able to cut the deficit back down just before the break.
Hughes ran in the Premiership side's bonus-point try after a rolling maul allowed the flanker to stretch over and add more to the Wasps' dominant lead, although Jackson missed the following conversion.