It was self-evident there was no love lost between the two teams as Greece walked out to an all-Croatian crowd at Dinamo Zagreb's Stadion Maksimir, and the star-studded Croats, backed by their fans, settled on the ball from the start.
Greece were pinned inside their own half and gave Croatia a taste of the rough treatment until they had a penalty given against them after 11 minutes. Watford keeper Karnezis extended his woeful week when he clumsily brought down Kalinic. Skipper Luka Modric stepped up to send the keeper the wrong way.
Croatia continued to turn the screw and they found their reward just moments later when Greece's woeful defending allowed Kalinic to be found inside the six-yard box and the AC Milan striker finished the move off brilliantly with his back-heel.
The visitors still found it in them to fight back and it looked like they were back in it when they scored with only their second chance of the game. Captain Sokratis rose above everyone else to head the ball into the back of the net and give his country hope. However, Croatia crushed the Greeks' World Cup dreams three minutes later, when Vrsaljko's cross was nodded in by Perisic who was completely unmarked at the back post.
In order to go into the return fixture as relaxed as possible, Croatia drove forward in search of more. Rakitic blazed his effort wide before a superb double-save by Karnezis allowed his side to go into the break with only a two-goal deficit.
The second half got underway and Croatia extended their lead almost immediately. Stafylidis chested the ball straight into the path of Vrsaljko and the Atletico full-back squared for Kramaric to tap in from close range.
A comfortable win for the team led by Modric, who could have furthered their lead in the final minutes. Mitroglou was twice denied the chance to reduce the deficit and give Greece hope going into the return fixture with Subasic getting down well to tap away at the base of the post.