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Leverkusen remain in third place in the table with 41 points, 11 behind leaders Bayern Munich and seven clear of Leipzig who currently occupy the final qualifying spot for next season's Champions League but have a game in hand.
Leverkusen opened the scoring in the 35th minute through Czech striker Patrik Schick who now has 20 league goals for the season.
Schick, however, was later forced off the pitch with an injury at the start of the second half.
Aaron Martin levelled for Mainz shortly before the hour mark but Lucas Alario restored Leverkusen's advantage in the 74th minute after being set up by Moussa Diaby.
Mainz refused to give up and levelled for the second time in the 84th minute through Dutchman Jean-Paul Boetius with Denmark's Marcus Ingvartsen hitting the shock winner with two minutes left.
