Narbekovas made his debut in 1983 with Žalgiris Vilnius, Lithuania's sole representative in the Soviet Top League, at the age of 18. In 1987, he finished second in league scoring with 16 goals while leading his club to a third-place finish, their best in history. Zalgiris would then participate in the UEFA Cup for the first time, losing to Austria Vienna.[2] Austria would become Narbekovas' destination after Lithuanian players were allowed to move abroad.