Moskvina became the Soviet national ladies' champion for the first time in 1962 and would win the title four more times. Her best finish at an international competition in singles was 14th at the 1965 European Championships. Moskvina may have been the first to perform what is now called a Biellmann spin. She was inspired after seeing a gymnastics competition and began attempting it on the ice. She included the spin at the 1960 European Championships.