The visitors began the game the better of the two sides, but the Tigers defended well to prevent their opponents from scoring.
Logo Mulipola scored a try to help the home side fight their way into the game, finishing the half strongly with Wasps' Tinus du Plessis in the sin bin.
Knowing that the win was safe, Leicester took a lot of their starters off, allowing Wasps to be more competitive in the closing stages of the game, Hugo Southwell securing a consolation try.
Vereniki Goneva went on to add a brace of tries for Tigers in the second half, ensuring a convincing win for the hosts.
However, the victory was marred by an injury to Tom Price, who has been taken to hospital to have his neck examined.