Igor Kharatin scored the only goal in the 26th minute of the match, bringing the first ever victory for the club in the UEFA Europa League.
In another Group J match, Sweden's Ostersunds beat Germany's Hertha 1-0 at home.
Oestersunds tops the table with six points after two rounds, with Zorya on three points, and Athletic and Hertha both on one point.
In the third round, Zorya will play Hertha at Arena Lviv on October 19.
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