Although League champions Gloucester took the lead with a fifth minute penalty from full back Wille Walker, the Tigers took complete control in the rain and were 22-6 to the good at half-time thanks to tries from scrum half Frank Murphy, wing Alesana Tuilagi and inspirational skipper Martin Corry.
It was more of the same after the break after Walker had kicked his third penalty. Andy Goode ran in try number four, Tuilagi got a second and then back row men Shane Jennings and Lewis Moody got in on the act.
Goode ended with a match tally of 19 points, while Gloucester had a consolation try from Ryan Lamb which Walker converted.
Leicester boss Pat Howard warned his players to curtail any celebrations until after their Heineken Cup final match with London Wasps never sunday saying, "We've got another one to go yet.
"Winning the Premiership is a lovely moment but we are focused on that other step next week.
"We'll go in as favourites but we have never beaten Wasps in a knockout game and we have to address that."