Leverkusen set new 33-match unbeaten record, go 11 points clear of Bayern Munich
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Andrich's goal was helped by a goalkeeping mistake from Mainz's Robin Zentner, who allowed the ball to slip through his hands and into the net.
Leverkusen were nervy and made a number of uncharacteristic errors, but the victory takes them 11 points clear of Bayern Munich in their bid for a first-ever Bundesliga title.
"We have to be honest and say we didn't play a great game and were a bit lucky to win, but we won't complain about the three points," Andrich told DAZN.