New Zealand paid the price for their sloppy fielding as skipper Cook took them to the cleaners, blasting a 47-ball 64, studded with two sixes and four boundaries.
Cook, who was dropped by Nathan McCullum thrice, anchored the England innings with two crucial partnerships. He forged a 75-run third wicket stand with Joe Root and then added 41 runs in 26 balls with Eoin Morgan for the fourth wicket.
But once he was caught and bowled by Nathan in the 19th over, England lost their way and could add only 28 runs losing the remaining six wickets.
More than half the match was lost after rains lashed Cardiff and the Sophia Gardens was mostly under covers throughout the day.
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Good work by the groundstaff enabled a late afternoon start after the rains relented, but sky remained overcast.
Interestingly, the toss happened at its scheduled time at 10 AM local time and New Zealand opted to field obviously keeping the weather forecast in mind.
The Kiwis will be guaranteed a place in the semis if they gain two full points.