Born into a Ukrainian family with Romanian roots, Gutsu started in gymnastics at age 6. She became a member of the national team of the Soviet Union in 1988. Her first major international competition was the 1991 World Artistic Gymnastics Championships in Indianapolis, where she won the team title with the Soviet Union and finished fifth in the individual all-around, while winning silver medals in two individual apparatus finals: the uneven bars and balance beam. Her silver on beam was highly controversial because the winner, Soviet teammate Svetlana Boginskaya, performed a simpler routine.