England jack-of-all-trades Austin Healey weighed in with a brace of tries, as did fullback Andy Goode, who also added six conversions and two penalty goals, to go with further tries from inside centre Ollie Smith and scrum-half Harry Ellis.
Wasps took an early lead via third-minute penalty goal from fly-half Alex King, only for Goode to draw level in the ninth minute with a three-pointer.
The visitors, however, were dealt a huge blow in the 18th minute when back rower Martin Corry was yellow-carded, with King adding three points and Stuart Abbott getting over for an unconverted try in Corry's absence.
But the Tigers hit back shortly before Corry's return from the sin bin, with Ollie Smith touching down and Goode converting – leaving the home side ahead by 11-10, before King made it 14-10 in the 31st minute.
Healey got his first score in the 34th minute, which Goode converted, putting the Tigers ahead for the first time and they never looked back after that, as Goode added another penalty on the stroke of half-time for a 20-14 lead.
All Wasps could muster in the second half was a single King penalty, as Leicester racked up another 28 points – through four converted tries, as Healey, Goode – and Goode again – got over, with little Ellis scampering over in the 73rd minute to complete his team's crushing victory.
With Bath, who beat Gloucester on Saturday, assured of a place in the Zurich Final on Saturday, May 29, Wasps now have to beat Northampton Saints to book their place in the Final, which will take place less than a week after the Heineken Cup Final against Toulouse – also at Twickenham.
Leicester, meanwhile, move into the Wildcard play-offs next Saturday, where they will face Harlequins.
For London Wasps:Try: AbbottPens: King 4
For Leicester Tigers:Tries: Smith, Healey 2, Goode 2, EllisCons: Goode 6Pens: Goode 2