The home side led 19-3 at the interval thanks to a blistering first-half performance and tries from Christian Wade, Tommy Taylor and Dan Robson.
Tigers fought back to within three points after Peter Betham's try.
After Dan Cole was sin-binned, Jimmy Gopperth's penalty secured the win.
The win took Dai Young's side back to the top of the Premiership table after Saracens' draw against Exeter on Saturday, with Leicester in fifth place after a third successive defeat.
However, Wasps, and England head coach Eddie Jones, will be concerned that flanker James Haskell, who was out for seven months because of injury, walked back off the pitch after appearing to be momentarily knocked out when tackling Freddie Burns.
Tigers will come away from the match with many positives under head coach Aaron Mauger, which did not look likely during the first-half blitz from Wasps.
Wade scored his ninth Premiership try of the season early on, before Taylor was put over in a drive and Robson crossed following a fast break out by man of the match Thomas Young.
After the break Tigers came out strongly, and after Betham finished off a move started by Tom Brady, Burns' penalty made it 19-16.
But Cole's yellow card for being offside helped the hosts regain some impetus, and Gopperth's kick from the resulting penalty made it a six-point game.
Tigers made late changes in search of a potentially decisive try, but poor handling from Betham and George Worth in particular cost them dearly.
The match attracted Wasps' best Premiership attendance of the season of 27,930, with the club having been watched by well over 50,000 supporters in two successive games at the Ricoh Arena for the first time.
Wasps: Beale; Wade, Daly, Eastmond, Bassett; Gopperth, Robson; Mullan (capt.), Taylor, Moore, Symons, Myall, Young, Thompson, Hughes.
Replacements: Johnson, McIntyre, Swainston, Gaskell, Haskell, Simpson, Cipriani, Miller.
Leicester: Burns; Thompstone, Betham, Roberts, Brady; O Williams, B Youngs; Genge, T Youngs (capt.), Cole, Slater, Fitzgerald, M Williams, Evans, O'Connor.
Replacements: McGuigan, Bateman, Cilliers, Kitchener, McCaffrey, Harrison, Worth, Smith.
Referee: Craig Maxwell-Keys (RFU)
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R&B Distillers has proposed turning Borodale House, a derelict Victorian hotel, into a distillery and visitor centre.
The building work is scheduled to begin in April this year and the production of whisky next year.
The distillery would be one of the largest employers on an island with a population of about 170 people.
James Haskell lasted just 35 seconds of his comeback game because of a head injury as Wasps held off a revival by Leicester, who were playing their first game since Richard Cockerill's sacking.
[NEXT_CONCEPT]
Highland Council has approved plans for the Isle of Raasay's first whisky distillery.