Iranian forward Shahab Zahedi, who has recently joined Zorya, scored the only goal of the match in the 34th minute.
Zorya Luhansk moved up to third place, seven points adrift of leader Dynamo Kyiv.
Zahedi, 25, joined Zorya on February 8 from Olimpik Donetsk
Another Iranian forward Allahyar Sayyadmanesh is also a member of Zorya Luhansk.