The big-serving Canadian, a semi-finalist at Melbourne Park last year, was clinical on a sun-bathed Margaret Court Arena, firing 21 aces and breaking the serve-volleyer from Luxembourg once in each of the first two sets.
Left-hander Muller, who celebrated his maiden ATP title in Sydney earlier this month in his 17th year as a professional, saved a match point in the decisive tiebreak but fired a forehand into the tramlines to bow out.
Highlights: Raonic through against Muller as draw opens up
Raonic will next play French 25th seed Gilles Simon for a place in the fourth round.
Meanwhile, David Ferrer survived the scare of the losing the first set to Ernesto Escobedo to set up a meeting with compatriot Roberto Bautista Agut in the third round.
Highlights: David Ferrer v Ernesto Escobedo
The 34-year-old went down 6-2 in the opening gambit but hit back to take the next three 6-4 6-4 6-2.