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Real Madrid teenager Martin Odegaard became the youngest ever European to start a non-friendly international match in history, but failed to make an impact as both sides felt each other out in the early stages.
Norway's hopes of producing a shock declined further when they had to substitute captain Per Ciljan Skjelbred after just a quarter of an hour because of injury.
Croatia took the lead on the half-hour mark through Marcelo Brozovic, who curled a low shot just inside the near post after a free-flowing team move by the home side.
Their lead was doubled not long into the second half and again it was a well-taken goal by the Croats as Ivan Perisic picked out the far corner from the edge of the box after a neat one-two with Ivan Rakitic.
Ten minutes later, it was three as Ivica Olic stabbed home from close range, leaving Norway with no chance of mounting a late fightback.
The visitors were given a glimmer of hope when they were awarded a penalty minutes later, but Tarik Elyounossi struck the post from 12 yards.
Vedran Corluka was yellow carded for his challenge that led to the penalty and five minutes later he was given his marching orders for a second bookable offence.
Norway took advantage of having more men on the field when Alexander Tettey pulled one back with 10 minutes to go, but they capitulated in the final stages.
Gordon Schildenfeld and Danijel Pranjic added further goals in the closing stages as Croatia ran out handsome winners to move three points clear and put the pressure on Italy, who play Bulgaria later tonight.