Second-half goals by Kingsley Coman and 18-year-old Jamal Musiala sealed the victory behind closed doors at Munich's Allianz Arena after Mainz took a shock early lead.
Bayern remain firmly on course to win the German league for the tenth straight season after stretching their lead at the top of the table as second-placed Dortmund drew 1-1 at Bochum.
Bayern boss Julian Nagelsmann enjoyed his 100th win in the Bundesliga as a coach, but the jaded hosts only took the lead 16 minutes from time.
"We made life hard for ourselves - you always have games like this, it's only human," admitted Thomas Mueller.
Bayern made a slow start, looking tired at the end of a busy week after last Saturday's 3-2 win at Dortmund and Wednesday's 3-0 win over Barcelona to secure a sixth win from six in the Champions League's group stages.
Mainz earned a shock 2-1 win over Bayern last April and the visitors took a deserved lead when Karim Onisiwo headed past Manuel Neuer after 22 minutes.
Bayern levelled when a long pass by Corentin Tolisso found Coman, who sprinted clear past Mainz goalkeeper Robin Zentner.
Bayern sealed the win when Musiala took his marker out of the game with a superb first touch and slotted past Zentner.
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