Xherdan Shaqiri also got in on the act as the defending champions moved seven points clear at the top of the Bundesliga standings following an ominously cut-throat display.
Third time lucky
Frankfurt survived an almighty scare just 20 seconds in when Mario Götze sent Müller through on goal, but the 25-year-old appeared to get caught in two minds and, not helped by an uncharacteristally heavy first touch, failed to find Robert Lewandowski with his eventual cross.
A Xabi Alonso free kick had the Eagles in a flap in the 15th minute and, although Müller was unable to make the most of the opportunity, the German World Cup winner stuck away the league leaders' next opening following a wonderfully flowing move involving Franck Ribery and Lewandowski.
The hosts looked to have resigned themselves to an afternoon of damage limitation, before Alexander Meier's dipping free kick at last gave Manuel Neuer something to think about between the Bayern posts. Normal service was nevertheless swiftly resumed, only for Lewandowski to fluff his lines from close range.
Pep Guardiola's men had won all 50 Bundesliga games in which Müller had been on the scoresheet and it looked like that run would continue when the visitors doubled their advantage in the 64th minute. Philipp Lahm clipped a stunning ball over the top for Ribery, who squared for Bayern's inimitable No25 to net his fifth league strike of the campaign.
Honing in on the second Bundesliga hat-trick of his career, Bayern's one-man goal machine was reeling away in celebration just three minutes later. Götze's pass was measured to perfection, with Müller duly holding off Timothy Chandler and firing beyond Frankfurt goalkeeper Felix Wiedwald for 3-0.
Götze and Jerome Boateng went close as the league leaders turned the screw, before second-half substitutes Arjen Robben, Sebastian Rode and Shaqiri combined to take the Bundesliga's pacesetters' emphatic haul to four for the afternoon and 27 for the season.
Line-ups and statistics