FC Ulisses 0-1 FC Sheriff
Serghei Gheorghiev scored the only goal just after the hour, giving Milan Milanović's side a narrow advantage to take into the second leg.
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FC Sheriff will start with a one-goal advantage over FC Ulisses in next week's UEFA Champions League second qualifying round second leg thanks to Serghei Gheorghiev's strike in Yerevan.
Gheorgiev scored with a powerful shot following Saša Marjanović's corner on the hour. Sheriff, beaten in the play-offs in each of the last two seasons, host their Armenian opponents in the return on Tuesday.
Both teams struck the crossbar in an even first period, Darwin Rios doing so for Sheriff midway through the half before Shota Jikia rattled the woodwork from captain David Grigoryan's cross. Sheriff, however, began to dominate territorially after the restart and gained their reward through Gheorgiev on 61 minutes.