Pep Guardiola's side crushed fourth tier minnows BSV Rehden 5-0 as they started the defence of one of three titles they claimed last season in impressive style.
Swiss playmaker Xherdan Shaqiri put Bayern on their way with just 18 minutes on the clock, before Muller doubled their advantage on the stroke of half-time.
The Germany international would go on to claim the match ball as he also stroked home from the penalty spot just before the hour mark and completed his treble on 64 minutes.
Mario Mandzukic got his name on the score sheet three minutes later and Arjen Robben rounded off the scoring two minutes from time.
Schalke also made it safely through to the second round on Monday, but were made to work considerably harder for a 2-0 victory at FC Nottingen.
Klaas-Jan Huntelaar broke the deadlock for the top flight outfit after half-an-hour, but they found the going tough against lowly opposition.
It was not until the third minute of stoppage-time that Leon Gotetzka struck to ease Schalke's nerves.
Elsewhere, Paderburn edged a 3-2 thriller against Duisburg and Union Berlin prevailed 2-1 on the road at Regensburg.