Balashov represented the USSR in several team events. He played on the second board for the USSR team at the 1971, 1972, and 1974 World Student Team Championships, winning the second board individual gold in 1971, when he was an international master, with a score of 6½/8 points. Balashov played in four European Team Chess Championships, 1970, 1973, 1977, and 1980, winning the individual gold on the fifth board in 1977. At the 24th Chess Olympiad in 1980, he scored 7½/10 as the first board reserve to help the USSR team win the gold medal.