Aleksandr Zavyalov made his international début at the 1978 Winter Universiade, where he won golds in the 30 km and relay. Next Zavyalov competed at the 1980 Winter Olympics, where he won bronze at 50K and was seventh in the 15 km. In 1980-81 Zavyalov won the World Cup, which he repeated in 1982-83. In 1982 Zavyalov competed at his only World Championships and won a gold in the relay, was second in the 15 km and was sixth at both 30 and 50 km. Zavyalov made his last international appearance at the 1984 Winter Olympics where he won silvers in both the 30 km and relay, was seventh at 50 km and 16th in the 15 km. Domestically Zavyalov won three Soviet titles – in 1983 at 30 km and in 1979 and 1982 in the relay. After his sporting career Zavyalov worked as a sports administrator and later served as President of the Russian Skiing Federation.