Having just turned 16, Turishcheva competed at the 1968 Summer Olympics, three years after she had started with gymnastics. She finished 24th in the all-around competition, but won the team gold medal with the Soviet equipe.
In 1970, she won the individual all-around world title, and the European title the following year, making her a favourite for the Olympic title in Munich in 1972.
There she was faced with the sudden popularity of her compatriot Olga Korbut. After Korbut fell from the balance beam, Turishcheva had no problems winning both the individual and team all-around titles. She was less successful in the apparatus events, qualifying for all four, but "only" winning a silver and a bronze.
After struggling with a back injury, Turishcheva won another all-around World Championship in 1975. At her third Olympics, she finished third in the all-around, second in the horse vault and floor exercise, and won the team all-around event for the third consecutive time, bringing her Olympic medal total to four gold, three silver and two bronze.
In 1977, she married sprinter Valeri Borzov, a two-time Olympic champion in 1972. Turishcheva is currently still involved in gymnastics, working for the Ukrainian federation.