Leicester edged Wasps to finish top of the Premiership for the first time since 2011 and set up a play-off semi-final against rivals Northampton.
Guy Porter's early score and George Ford's conversion were the only points of the first half at Welford Road.
Jimmy Gopperth's penalty cut the gap, but Freddie Steward's try and Ford's penalty put the Tigers 17-3 ahead.
Will Porter finished a rapid break as Wasps hit back, but a further Ford penalty sealed a 20-10 win.
Leicester, who have won every home league game this campaign, will host East Midlands rivals Northampton in the play-offs next Saturday after the Saints clinched fourth spot.
Wasps will have to settle for a place in the European Challenge Cup next season after a ninth-placed finish.
Tigers have led the standings since the early weeks of the campaign and finished seven points clear of Saracens who started the day three points back but fielded a weakened side and were thrashed at Gloucester.
The home side began with real intent and crossed after just three minutes when Ford fed Porter who attacked the line at pace and broke through two tackles to waltz in under the posts.
But any thoughts the floodgates would open were quashed by a Wasps side looking for points to sneak into the top eight and secure a place in the Champions Cup qualification for next season.
Defences took charge of a physical big-hitting wrestle for territory, forcing mistakes which became endemic in a messy first half befitting the opening round of the season rather than the regular season finale.
Both sides created line breaks and half-chances, but precision was lacking, Ford underlining an error-strewn first half when he scuffed a penalty kick wide of the posts just before the break.
A scoreless 46 minutes was broken when sustained pressure earned Wasps a penalty which was slotted by Gopperth, making his 156th and final appearance against the team he will join next season.
Tigers just about withstood a surge towards their own line as the visitors continued to press for scores, but again, both sides traded errors and turnovers as soon as opportunities beckoned.
Matias Moroni was brilliantly held up over the line by Wasps fly-half Charlie Atkinson and from the following play, the hosts worked an overlap for Steward to dive over in the corner.
With confidence renewed, the Tigers looked to have turned the corner, but a swift break and fine offloads allowed Porter to dot down seven minutes after coming on and reduce the deficit to 17-10.
A second Ford penalty eased any nerves as Leicester finished the regular season with a perfect home record of 12 wins for the first time since 2001-02.
However, head coach Steve Borthwick will know his side will need a much improved performance if they want to reach Twickenham on 18 June.
Leicester head coach Steve Borthwick:
"Clearly with the execution we want to be better, but in terms of the nature of the contest it was a great contest.
"I thought there were some positive elements, but it was clunky overall. I think we missed opportunities but I think both teams struggled with that downpour before kick-off.
"Quite a lot has come out from Northampton, they're thinking about finals rugby. What we will do is, we will enjoy this. I've said to the players you've got to enjoy the win, keep enjoying the wins."
Wasps head coach Lee Blackett:
"We made too many mistakes with the ball. Too many skill errors that you wouldn't expect and that was the thing.
"I thought our set-piece, something we've been working really hard on, I think it's showing itself at the moment. We've worked so hard on it that that's putting us in great field position.
"There were some positives around the kicking game and some things we definitely needed to fix up. We're getting field position but what we're doing with the ball was kicking it back and not taking advantage of that."
Leicester Tigers: Steward; Ashton, Moroni, Porter, Potter; Ford, Youngs, Genge (capt), Clare, Cole, Chessum, Green, Martin, Liebenberg, Wiese.
Replacements: Cowan-Dickie, Leatigaga, Hurd, Wells, Reffell, Van Poortvliet, Burns, Nadolo.
Wasps: Crossdale; Odogwu, Spink, Gopperth, Bassett; Atkinson, Robson, West, Oghre, Alo, Launchbury (capt), Gaskell, Shields, J Willis, T Willis.
Replacements: Frost, Hislop, Millar-Mills, Fifita, Barbeary, Porter, Miller, Fekitoa.