Twelvetrees, playing at fly-half for Tigers in place of the injured Toby Flood, pounced for two tries, five penalties and two conversions, as the home side overcame a sluggish start to run out comfortable winners in cold, blustery conditions.
Leicester, without Flood and fellow injured England players Manu Tuilagi and Louis Deacon, were never at their most fluent, particularly behind the scrum, but they were still too much for Wasps.
Second-bottom Wasps had made a solid start, belying their lowly league standing, and the home side took the best part of half an hour to find their feet.
Elliott Daly and Twelvetrees exchanged early penalties, before Wasps scored the opening try after 14 minutes as winger Tom Varndell rescued a move which looked to have broken down.
He made good ground down the left before Nic Berry was able to charge over untouched to put his side 8-3 up.
After pulling a penalty back, Twelvetrees provided the spark his side and the match needed.
His well-timed pass put Geordan Murphy into a gap and opened up the Wasps defence. The Irishman's inside pass to Thomas Waldrom went to ground off Varndell making the covering tackle, and Twelvetrees was quickest to react, picking up the ball to dive over and put his side 11-8 ahead.
He converted his own try, then exchanged penalties with Wasps fly-half Ryan Davis as Tigers went to the break 16-11 up.
The second half again saw Wasps start well, applying pressure on the Leicester line, but as with the first half they lacked the ability to really punish their hosts.
And it was not long before Tigers asserted real dominance, controlling the tempo and possession to eventually close out the game in a relatively comfortable fashion.
Twelvetrees kicked another two penalties as Tigers edged out to a 22-11 lead, the second resulting in Wasps prop Tim Payne being sent to the sin-bin with 20 minutes remaining.
Leicester looked to make the most of their numerical superiority, launching a series of raids on the Wasps line.
Anthony Allen and Geordan Murphy both went close, and Wasps resisted until the 72nd minute.
Inevitably it was Twelvetrees who provided the coup de grace, but he had plenty of help from his inside-half partner.
He bagged his second try of the night following yet another series of determined attacks on the Wasps line, collecting a smart pass from England scrum-half Ben Youngs to score right under the posts, and converted his own try to put the seal on a convincing victory.
Leicester's win moves them level on points with third-placed Northampton, while Wasps remain second from bottom but still 10 points clear of bottom placed Newcastle Falcons, who lost at home to Exeter.
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