Jonny Wilkinson kicked over all of the home side's points as they set up an away encounter with Saracens at Twickenham Stadium in the last four.
Three penalties from Toby Flood gave the visitors a 9-0 lead with 18 minutes on the clock before two kicks from Wilkinson reduced the home side's deficit at half time.
Two more penalties from Wilkinson then edged Toulon in front, but Flood made the score 12-12 with 58 minutes played.
However, Wilkinson edged ahead in the battle of the kickers moments later to put the hosts on top once more and extended their advantage further with 10 minutes to play.
Flood added another three points to Leicester's tally late on, but Wilkinson had the final word as a drop goal capped a dominant performance from the Englishman.