The basement side enjoyed a fine start at Welford Road, scoring the game's first try through Marland Yarde after five minutes, but they failed to build from there.
George Ford's boot proved decisive for Leicester as he dispatched four penalties, seemingly putting the Tigers out of sight after Kyle Eastmond went over from Gareth Owen's offload.
Sale came into the contest again in the final 20 minutes and crossed through both Rob Webber and Curtis Langdon, but Will Cliff was unable to land any of his three conversion attempts.