The Germany international stuck three times as the Bavarians began the defence of their DFB-Pokal title by hammering fourth-tier minnows Schwarz-Weiss Rehden
Switzerland international Xherdan Shaqiri opened the scoring after 18 minutes before Muller bagged his first in the 45th minute.
And the German claimed his hat-trick in the first 20 minutes of the second half with two more goals before Dutchman Arjen Robben put the finishing touches on the big win with a late strike.
"We’re satisfied with the 5-0 result and I'm delighted I scored a couple of goals," said Muller after the match. "We're in good shape and heading in the right direction.”
Coach Pep Guardiola also expressed his satisfaction with the result after Bundesliga sides Werder Bremen, Borussia Monchengladbach, Nurnberg and Eintracht Braunschweig all exited the competition at the first hurdle on Sunday.
“Cup ties are always dangerous. Four Bundesliga clubs were knocked out yesterday," he said.
"I'm aware of which club I’ve joined, we have to win every match, but that's normal. People always want more. I accept the pressure. We've only been together seven weeks so we still have to improve a lot.”