Iranian forward Allahyar Sayyadmanesh, who has recently joined Zorya Luhansk from Fenerbahçe, scored six minutes from time to inflict a first defeat on the Foxes in the competition.
Leicester remains top of Group G thanks to its head-to-head record against Braga and will finish first if it wins at home to rock-bottom AEK Athens in the final group game next week.
Zorya failed to book a place in the next stage and remained in third place.