They hit the post through Borja Iglesias in the 87th minute before Germany international Andrich stabbed in the equaliser a minute later.
Schick completed the comeback with a far-post volley in stoppage time.
The result means that Leverkusen now have the second longest unbeaten run in the history of Europe's top-five leagues, overtaking the 2004-05 Inter Milan team who managed 38 games.
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