Bayern, who became the first German team to win the Champions League as well as the domestic double last season, start their Bundesliga season against Borussia Moenchengladbach on Friday.
The Bavarians were by no means firing on all cylinders when Xherdan Shaqiri tapped in from close range for the lead in the 18th minute.
Mueller then struck three times, including a spot kick as the amateurs fought desperately but could not match their opponents' pace and quick passing.
Arjen Robben completed the scoring with a low shot two minutes from time.
Schalke 04 also joined them in the second round after battling to a narrow 2-0 win against fifth-tier Noettingen.
It was the underdogs who twice hit the woodwork in the opening minutes and Schalke had to wait until the 30th minute to take the lead through Klaas-Jan Huntelaar.
New signing Leon Goretzka added another in the last minute to seal a less than convincing win.
Fellow Bundesliga heavyweights Borussia Dortmund and Bayer Leverkusen had already booked their spots in the next round over the weekend but several top tier clubs crashed out including Werder Bremen and Borussia Moenchengladbach.