Pep Guardiola's men - contesting the FIFA Club World Cup final in Morocco - will have been boosted by news from home that both Borussia Dortmund and Bayer Leverkusen suffered league defeats against Hertha Berlin and Werder Bremen respectively.
The results leave Bayern seven points clear at the summit with a game in hand over their closest rivals.
In Dortmund, Marco Reus got the game off to the best possible start for Jurgen Klopp's side as he slotted home in the seventh minute, but Adrian Ramos pulled the visitors level from close range midway through the first period.
With just one win from five Bundesliga outings, Dortmund will be feeling the pressure, but, on a bad day for the division's leading clubs, Leverkusen were unable to take advantage of that slip-up as they fell to a second successive reverse.
Sami Hyypia's charges looked second best throughout in a 1-0 defeat to Bremen as Santiago Garcia's 75th-minute strike proved to be the difference between the sides.
Rafael van der Vaart appeared to have at least rescued a point 11 minutes from time, but Tomas Rincon's dismissal for a second bookable offence three minutes later was followed by a Mainz injury-time winner from Okazaki.
Elsewhere, 10-man Eintracht Braunschweig momentarily pulled themselves off the bottom of the league with a 1-0 victory over Hoffenheim, but now sit at the foot of the table on goal difference following Nuremberg's goalless draw with Schalke, who missed the opportunity to climb to fifth.
Freiburg also picked up a vital three points as Admir Mehmedi's first-half double inspired them to a 2-1 win against Hannover.
