The Bavarians made three changes from the win over Augsburg, as Leroy Sane, Niklas Sule and Alphonso Davies were all recalled.
The game was open in the opening exchanges and shot-stopper Ralf Fahrmann made a double save in the 23rd minute to deny first Robert Lewandowski's whipped effort and kept out a follow-up from Serge Gnabry on the rebound.
Muller eventually broke the deadlock for Hans-Dieter Flick's charges in the 33rd minute with a header at the back post after a teasing cross by Joshua Kimmich.
Bayern were pressurising Schalke in the closing phase of the first stanza but the visitors were spirited in defence and kept them at bay to go the break only trailing by one goal.
Lewandowski doubled the Bavarians' lead nine minutes from the break with a strike past underneath the dive of Fahrmann from a tight angle after a through ball over the defence by Kimmich.
Bayern were a constant threat after that creating plenty of chances but they did not have the finishing touches to put the game to bed yet while Schalke were struggling to test Manuel Neuer.
However, Muller sealed the three points for Bayern in the last two minutes with a header from Kimmich's free-kick to complete his brace.
David Alaba rounded off the scoring for Flick's men in the last minute with a long range strike as the defending champions moved seven points clear of second-placed RB Leipzig.
