After a tight early period, recently returned Ross Taylor scored an impressive 100 from 117 balls while Brendan McCullum, who has replaced him as captain, smashed a lambasting 74 from 36 balls.
Kane Williamson at number three was the only other Black Cap batsman to trouble the scorers with 33 before the hosts were bowled out for 269 from 48.5 overs.
James Anderson starred with the ball for the tourists finishing with figures of five for 34.
The hosts struggled to find what the Englishman so beautifully utilised in the pitch before their batsman ran down the total in 47.4 overs with significant partnerships – Cook and Bell 89, and Cook and Trott 50, before Trott and Root finished the job.
The teams meet for the series decider in Auckland on Saturday at 1am (GMT) ahead of their three-Test series in NZ and then a Test and ODI series in England leading into the Ashes.
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