The visiting pack went close on several occasions against a well drilled home pack before Leicester regained the lead when Lucas Guillame pushed his way over. Henry Purdy then sent Tigers further ahead just before the break with a superb finish.
Mathew Tait marked his return to action after a lengthy spell out with a try early in the second half before Cavaliers responded again as they kept possession through a number of phases close to the Tigers tryline before Young stepped inside the covering defence to score under the posts. Carlisle added the extras as the visitors trailed 22-14.
Purdy secured the game as he finished a sweeping move before Lewington and Williams scored late tries to complete a home victory.