Mueller’s opening goal on the rebound in the 22nd minute was a bad omen for Frankfurt, with the attacking midfielder having scored in 50 previous Bundesliga games of which Bayern had won 47 and drawn three.
The Germany international doubled the visitors’ lead when he tapped in a Franck Ribery pass in the 64th but Bayern, who booked their spot in the Champions League last 16 this week with a win over AS Roma, never hit top form.
Mueller completed his hat-trick three minutes later when he raced clear to beat Felix Wiedwald for his sixth goal of the season.
Xherdan Shaqiri then deflected a Sebastian Rode shot into the goal as Bayern won for the sixth time in seven league games.
“After a Champions League game it is always a bit difficult, “We had our problems at the start,” coach Pep Guardiola told reporters.
“Now we have a few days (with the break for international matches) to sit down in peace and quiet and analyse what we can improve further.”
The Bavarians are top on 27 points with second-placed VfL Wolfsburg and Borussia Moenchengladbach in third, both on 20 and in action on Sunday.
Bayer Leverkusen failed to replicate their winning Champions League form from midweek and had to settle for a goalless draw against Mainz 05. They dropped to sixth on 17 points.
Hoffenheim are also on 17 having lost 4-3 to Cologne after coming back from 3-1 down to level with a double from Roberto Firmino in a roller-coaster game.
Champions League side Schalke 04 continued their erratic form and slumped to a 2-0 loss at Freiburg to drop to 11th on 14 points.
It was second successive loss for Schalke after going 4-2 down against Sporting in the Champions League.
(Reporting by Karolos Grohmann; editing by Ed Osmondb)