Moving up to featherweight, Davidyan won the 1973 European Championship and then, moving up again to lightweight, won the 1974 World Wrestling Championships as a last minute replacement for Shamil Khisamutdinov. After the 1974 World Championships, Davidyan switched back to featherweight and competed in this class until the end of his career in 1981. After moving back to featherweight, Davidyan won the 1975 World Wrestling Championships as well as the 1975 and 1976 Soviet titles. Davidyan won a silver medal at the 1976 Summer Olympics in Montreal.