Capped 50 times by Yugoslavia between 1959 and 1966, Durković excelled as a 22-year-old at the first UEFA European Championship, offering defensive solidity and attacking penetration at right-back. Although Yugoslavia finished second in France, Durković won a gold medal at the Rome Olympics the following September. He also wore the number two shirt at the 1962 FIFA World Cup in Chile and was an ever-present as Yugoslavia eliminated former winners Uruguay and West Germany and finished fourth. Durković played with Red Star Belgrade until he was 28 at which point he moved abroad and made a name for himself with AS Saint-Etienne, winning three French League titles and the Coupe de France twice. He died when mistakenly shot by a policeman in Sion, Switzerland in June 1972 at the age of 34.