David Mele scored the bonus-point try three minutes from time as Tigers consolidated their third-placed position in the Aviva Premiership table.
Manu Tuilagi scored the opening try of the game during the first half and Vereniki Goneva, who extended his contract at Tigers earlier in the day, celebrated his new deal with his 12th score of the campaign.
England and Lions centre Tuilagi rumbled over for his second try nine minutes into the second half but Tigers were made to work for Mele’s bonus-point score by a determined Wasps side, who scored two tries of their own through Guy Thompson and Tommy Bell.
The result moved Tigers three points behind second-placed Northampton Saints in the table with three rounds left to play.
Geoff Parling and Niall Morris returned from injury to take their place among the replacements for Tigers.
Tigers made three changes in the pack with Boris Stankovich and Fraser Balmain coming into the front row and Graham Kitchener joining captain Ed Slater in the second row. Matt Smith came into midfield alongside Manu Tuilagi in the only change to the backline.
Wasps settled quickly into the game. Andy Goode, on his return to Welford Road, turned down an early long-range penalty for territory and it paid off as Nathan Hughes collected the lineout and rumbled into the Tigers 22 where Leicester were pinged in front of their posts. Former Leicester fly-half Goode slotted a simple penalty to put the visitors into an early lead.
A break by Tuilagi from a ruck on the Leicester 10m line took Tigers up to the Wasps 22. Smith tried to find a gap down the narrow channel but was tackled into touch.
Tigers made a mess of the Wasps lineout to steal possession. Vereniki Goneva stretched his legs for the first time before Blaine Scully was bundled into touch 10m out.
Tigers made it difficult for Wasps to clear the ball from their half and kept up the pressure through Tom Youngs’s barrelling run. Carlo Festuccia, on as a blood replacement for Tom Lindsay, came in at the side of a ruck to concede the penalty but Williams’ kick was short in blustery conditions.
Great work by Kitchener, charging down two attempted kicks by scrum-half Charlie Davies, kept Wasps pinned near the edge of their own 22.
And Tigers eventually made the pressure tell midway through the half. Kitchener claimed lineout ball to set up the drive which rumbled some 15 metres into the Wasps 22. The drive continued to go forward but Ben Youngs opted to play and his pass allowed Tuilagi to burst through the tackle and score under the posts. Williams landed the extras as Tigers led 7-3.
Wasps hit back from the restart. Davies appeared to have found a gap between Stankovich and Slater but the Tigers captain made the ground to complete the tackle. Wasps flooded forward and Will Helu seemed certain to score when he collected Tom Palmer’s offload but brilliant defending by Tuilagi saw him make up a couple of metres on the Wasps wing, effect the tackle and hold his man up over the line in the same movement.
Wasps did have their try 12 minutes before the break. Ed Jackson's neat hands picked up a loose ball off his toes and he found Thompson on an angled line past Scully and over to the left of the posts. Goode landed his conversion to put Wasps into a 10-7 lead.
Scully rose above Helu to claim the restart in the Wasps 22 and for a moment looked to have burst through to the line. But he was tackled 8m short where the visitors went off their feet. Gibson set up the drive from the lineout but Tigers lost possession just short of the line and Davies cleared.
Tigers hammered away at the Wasps defence as they looked for a score before half-time. But they met stern resistance, with Palmer robbing Goneva of possession as the wing tried to force his way through a gap on the Wasps 22.
Tait got through plenty of work with ball in hand and it was his dart down the left onto Goneva’s pass that created Tigers’ second try. Tait returned the pass to Goneva on his inside and the Fiji international held off Tommy Bell and James Short to score at the left corner. Referee Andrew Small consulted his television match official before awarding the score.
Williams landed a testing conversion from the left touchline with the last kick of the half to send Tigers in at the break 14-10 ahead.
Tigers introduced Marcos Ayerza and Logovi’i Mulipola from the bench early in the second half in place of Stankovich and Balmain respectively.
But it was good work by the locks that secured possession at a Wasps lineout midway inside the visitors’ half to set Tigers back on the attack. Crane sucked in a couple of defenders before Tuilagi broke Festuccia’s tackle and then held off James Short and Davies to score his second try of the game. It went unconverted as Tigers led 19-10.
Tigers rejigged the backline with Toby Flood replacing Smith. Flood slotted in at 12 with Tuilagi moving across to 13. David Mele then replaced Ben Youngs as a stop-start second half approached the last 20 minutes.
Mele was alert to an overlap on the left flank, getting across to halt Hughes as the No8 bore down on the Tigers 22.
There was a huge reception for Parling as he returned to the action following his injury lay-off for the final 18 minutes, the England and Lions lock replacing Kitchener.
Festuccia was pinged for failing to release Goneva in the tackle and Williams landed the kick from 40m to move Tigers 22-10 ahead.
But Wasps were not finished yet and they put Tigers under pressure with a couple of close-range lineouts. But Tigers defended the drive well and then won the scrum put-in as Wasps tried to run the clock down at a ruck.
Rob Hawkins and Pablo Matera replaced Youngs and Crane for the final 10 minutes.
Wasps gave themselves a lifeline with a neat try off the back of a scrum. Eliot Daly slipped a lovely grubber kick into the left-hand corner where Tommy Bell won the foot race to dot down their second try of the game. It left Tigers 22-15 ahead with eight minutes remaining.
The decibel levels increased around Welford Road as Tigers pressed from the restart searching for the bonus-point try. Goneva’s charge was stopped 5m short of the line before Hawkins knocked-on under pressure at the next phase.
A high tackle on Scully gave Tigers the chance to kick for the corner with three minutes remaining and set up one final push for the bonus-point score.
Gibson collected lineout ball and Matera was in control of possession at the back of the drive before Mele eventually applied the finish at the right-hand corner.
It was Mele's fourth try for Tigers and secured a seventh victory in a row in the Aviva Premiership for Richard Cockerill’s men.