Bleznitsov won two medals at the Universiade, winning the 1963 title in a championship record of 4.60 m before taking a silver in 1965 behind American John Pennel. He was the inaugural pole vault champion at the annual 1966 European Indoor Games and won three silver medals in the subsequent years, beaten by fellow Soviet Igor Feld and East Germany's Wolfgang Nordwig. He was twice a medallist at the European Cup and competed at the 1966 European Athletics Championships, though he failed to register a height.