Boos rang around the stadium at the final whistle and the result will pile more pressure on Turkey coach Guus Hiddink who was already under fire after a patchy campaign in the qualifiers in which they finished second in Group A.
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 and the evening did not get any better for the Turks.
"Nobody can expect a result like this when they come to Turkey," Croatia coach Slaven Bilic, who patrolled the technical area in a smart suit and bobble hat, told reporters.
"We know Turkey is a very emotional team and we are too so that goal lifted us."
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.
Goalkeeper Volkan was jeered in the latter stages of the game and their were chants for Hiddink's resignation.
"It was almost decided in the second minute because they are a very experienced Croatia team and they play in the strongest leagues in Europe," Hiddink said in a post-match TV interview.
"We ouplayed them for a while but the second on the counter-attack before half-time made it very difficult to overcome them," he added. "It's almost decided now but maybe we will start some new players and they will play for the honour of themselves."
