Galina Shamray took up gymnastics in the 1940s and quickly became the regional champion of Uzbekistan in the Soviet Union. She became the junior national all-around champion in 1950 and then advanced to the senior national team. She was selected to represent the Soviet Union at the 1952 Helsinki Olympics, where she won gold in the team all-around and silver in the team portable apparatus. Individually, her best finish was seventh in the uneven bars. At that year’s senior national championships, she was runner-up in the floor exercise, while in 1953 she was fourth in the all-around.
Shamray’s greatest year was 1954, when she became the first Soviet woman to win the all-around title at the World Championships. She also helped her country capture the team all-around title and took silver in the uneven bars and the team portable apparatus at that tournament. She won the Soviet balance beam title in 1955 and was runner-up in 1956, at which point she retired from active competition and married Olympic football champion Anatoly Ilyin. She later had an extensive coaching career, and was also an international gymnastics judge, most notably at the 1980 Moscow Olympics.