Jhon Cordoba snatched the winner for the visitors in the 86th minute.
"The game was a clear indication that it's not easy to win in the Bundesliga," said Bayern coach Pep Guardiola." Congratulations to Mainz for the victory.
"In the second half it wasn't easy, with 10 players in their penalty area, but we had enough chances to win the game. We still have much work to do to defend our title."
Borussia Dortmund closed the gap at the top to five points as they beat SV Darmstadt 98 2-0 ahead of the second-placed club's meeting with Bayern on Saturday.
Pep Guardiola's men gave a lacklustre display and Mainz, who are fifth in the table, went 1-0 up when Jairo Samperio arrived at the far post to hammer Giulio Donati's cross past keeper Manuel Neuer in the 26th minute.
Bayern, who were last beaten by Borussia Moenchengladbach on Dec. 5, levelled thanks to a 25-metre drive from Arjen Robben in the 64th minute.
The 32-year-old Dutchman was set up by Arturo Vidal and Robben controlled the ball before hitting a thunderous left-foot shot to notch his first goal since November.
Bayern pushed for a second goal but Mainz hit them on the break as Daniel Brosinski found Julian Baumgartlinger and his cut-back was converted from the edge of the area by Cordoba.
Mainz now have 39 points from 24 matches, three behind third-placed Hertha Berlin who beat Eintracht Frankfurt 2-0 thanks to second-half efforts from Mitchell Weiser and Salomon Kalou.
Bayern are on 62 points while Dortmund have 57.
Adrian Ramos' first-half header gave Dortmund a 38th-minute lead at Darmstadt, the striker flicking Gonzalo Castro's fine curling ball past Christian Mathenia, before Erik Durm finished from close range after more good work by Castro.
"The victory gives us an enormous boost," said visiting coach Thomas Tuchel.
Gladbach remained fourth on 39 points after outclassing Stuttgart 4-0 while Schalke 04 defeated Hamburg SV, who had Johan Djourou sent off in the 45th minute, 3-2.
Bayer Leverkusen lost 4-1 at home to Werder Bremen while relegation-threatened Hoffenheim sank Augsburg 2-1 with Mark Uth grabbing the 81st-minute winner.
(Editing by Tony Jimenez)
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