The tie, which was played without any visiting Serbian fans because of the fear of violence, was crucial as the visitors looked to haul themselves back in contention to qualify for the World Cup.
However first half strikes from Ivica Olic and Mario Mandzukic ensured Croatia took another decisive step towards qualification.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.