Gutsu starting participating in gymnastics at age 6, and became a member of the national team of the Soviet Union in 1988. Her first international championships were the 1991 World Championships in Indianapolis, where she won the world title with the Soviet team and finished fifth in the individual all-around, while winning silver medals in two apparatus events.
In the next season, before the 1992 Summer Olympics, Gutsu won European titles in the all-around, balance beam and horse vault. Now one of the favourites for the Olympic all-around title, the 15-year-old Gutsu almost missed the final of that event. In the preliminaries, Gutsu fell from the balance beam and placed 9th. Although 36 gymnasts qualified for the final, only 3 competitors from each country were allowed in the final, and three other competitors of the Unified Team placed higher than Gutsu. However, Rosalia Galiyeva forfeited her place in the final because of an knee injury—though probably faked.
Gutsu became involved in a close finish for the gold medal. With one apparatus to go, Gutsu was tied for first place with two others trailing less than four tenths. Gutsu's final performance was just enough to hold of a challenge of America's Shannon Miller to win the title by 0.012 points. Gutsu won additional medals in the team all-around (gold), uneven bars (silver) and floor exercise (bronze).
After her gymnastics career, Gutsu moved to the United States, where she now is a gymnastics coach.