 Durković akaonekwa kanokwana makumi mashanu neYugoslavia pakati pa1959 na1966, Durković akabudirira semakore makumi maviri nemaviri ekuberekwa pa UEFA European Championship yekutanga, inopa kuzvidzivirira kwakasimba uye kupinda kunopinda kurudyi-kumashure. Kunyange zvazvo Yugoslavia yakapedza iri yechipiri muFrance, Durković akawana menduru yegoridhe paMitambo yeOlympic yeRoma muna September akatevera. Akapfekawo hembe yechipiri paFIFA World Cup ya1962 muChile uye aigara aripo sezvo Yugoslavia yakabvisa vakundi vekare Uruguay neWest Germany uye vakapedza chechina. 