Bundesliga: Eintracht Frankfurt 0 Bayern 4
A strong start from the visitors was rewarded midway through the first half when some good work from Franck Ribery allowed Muller to tap home.
Despite a couple of scares before the break, the visitors rarely looked troubled, and Muller was on hand to double the lead just after the hour, slotting home after again linking up with the imperious Frenchman.
And the 25-year old completed his hat-trick three minutes later after being played in by Mario Gotze, with Xherdan Shaqiri's strike compounding the misery of Thomas Schaaf's side, who have now lost five on the bounce.
The win extends the champions' unbeaten run to 17 games in all competitions, leaving them seven points clear at the top of the table.
Having sealed their place in the last 16 of the UEFA Champions League with a 2-0 win over Roma in midweek, Pep Guardiola's men began proceedings at the Commerzbank Arena with predictable confidence, keeping the ball with very little effort during the opening 15 minutes.
Ribery provided much of the early pressure for the visitors, getting behind the defence several times early on as Bayern looked to build on a rampant recent run that had seen them net 23 goals in their first 10 games.
Despite a spirited rearguard display from the hosts, the Frenchman continued to cause problems, and he was at the centre of Bayern's opener after 22 minutes.
A bursting run down the left flank allowed the winger to tee up Muller with a low cross and he tapped home from close-range after Felix Wiedwald's initial save.
Frankfurt had not scored against Saturday's opponents in nearly 400 minutes of competitive football coming into the game, and they showed little sign of changing that record until the 40th minute.
Some excellent work on the left flank saw Haris Seferovic shake off the attention of Rafinha, but his low ball towards the near post was denied by a combination of Manuel Neur and Dante.
Neur was called upon again just two minutes later, denying Alexander Meier's low free-kick with a full-stretch save.
But that was as good as it got for the hosts, with Bayern quickly resuming control of the game after the break.
And Guardiola's men doubled their lead after 64 minutes when a dinked ball over the top found Ribery behind the defence, and his squared pass was swept home by the impressive Muller.
And a terrific afternoon for the German was completed six minutes later when Gotze's superb pass cut through the heart of the home defence, allowing the forward to slot home with aplomb.
Bayern's second away league triumph of the season was rounded off four minutes from time as former Frankfurt man Sebastian Rode set up fellow substitute Shaqiri, who fired home with a low drive inside the box.