Olic put the visitors ahead in the second minute with a simple tap in from close range after goalkeeper Volkan Demirel failed to cut out a low cross from Vedran Corluka.
Despite a long period of Turkey possession, Croatia doubled their lead in the 32nd minute when Mandzukic headed in a cross from Darijo Srna at the far post.
Turkey’s misery was complete in the second half as Corluka made it 3-0 in the 51st minute, escaping his marker and heading in from close range from a free kick whipped in by Srna.
The return leg will be in Zagreb on Nov. 15 although few of the Turkish fans inside the Turk Telekom stadium will retain much hope that their team can turn the tie around.
Their were chants for Hiddink’s resignation at the end while goalkeeper Volkan was also jeered.
It was an especially sweet victory for Croatia who suffered a heart-breaking quarter-final defeat by Turkey at the 2008 finals when they were seconds away from clinching a semi-final berth before losing the clash in Vienna on penalties.
The Turks had equalised with the last kick of extra time and then won the shootout.
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