The Tigers bounced back from last week's Heineken Cup exit in Toulon in some style thanks to a pair of tries from England scrum-half Ben Youngs, and further scores from Graham Kitchener, Rob Hawkins and Adam Thompstone.
A badly-depleted Wasps side, who were under the cosh for most of the game, scored just one try through Elliot Daly, the rest of the points coming from the boots of Daly and Chris Bell.
The Tigers started brightly thanks to centre Anthony Allen, who cleared up a messy situation in his own 22 and made a fabulous break after shaking off two tackles which resulted in a line-out near the Wasps' line. Leicester failed to take advantage of their good attacking position and then fly-half Toby Flood missed an easy penalty from right in front of the posts.
He did, however, make amends from the same spot in the 14th minute before adding a second penalty five minutes later to give Leicester a 6-0 lead.
Leicester then hit Wasps with two tries in the space of five minutes, the first coming from Youngs, who darted over from a ruck after some intense pressure by the Tigers. Kitchener got the second after Leicester switched play from right to left, allowing the big lock forward to barge straight through tiny winger Christian Wade. Flood failed to convert both tries.
Wasps lost both Wade and fly-half Nick Robinson, who were injured in the build up to the tries but, in the 29th minute, they got on the scoresheet thanks to a long-range penalty from Bell. Leicester, however, hit back seven minutes later when hooker Rob Hawkins got on the end of a rolling maul for Leicester's third try, which Flood failed to convert again.
Bell kicked his second penalty a minute from half-time but lasted only four minutes of the second half before being sin binned for a deliberate knock-on while attempting to lift a siege of the Wasps' line.
From the resulting scrum, Youngs darted over for his second try, which Flood converted, earning the Tigers a bonus point before Daly banged over a long-range penalty for Wasps.
It was all Leicester at this stage and, in the 59th minute, Thompstone stormed down the left wing for Leicester's fifth try which Flood converted to make it 35-9. As more replacements came on the field, the game started to open up and Daly's pace earned him a terrific try in the 62nd minute, which he converted himself.