But Jos Buttler s dashing unbeaten 61 off 48 balls, including a couple of extravagant sixes, helped take them to 310 all out. In a scratchy 23-ball knock, he managed 13 runs, hitting two boundaries in it before he was castled in the eighth over by Adam Milne (3-79).
Luke Ronchi went for a golden duck to Ball but - after Martin Guptill was removed for 27 - skipper Williamson and Ross Taylor (39) calmed matters brilliantly.
England has won nine of its last 10 ODI matches (L1) whilst New Zealand has claimed wins in 10 of its last 14 completed ODIs (L4). The partnership rode on Williamson's shoulders, but when he fell to Wood, New Zealand needed 153 more from 118 balls - a task beyond the rest of the batting line-up.
But while Williamson's wicket made the final difference, victory was set up by England's powerful batting effort after being put in to bat.
Their wins over Bangladesh and New Zealand means they are confirmed as group winners, even before they meet Australia at Edgbaston on Saturday, due to the number of victories they have recorded.
Earlier, Root hit four fours and two sixes before chopping the ball back onto his wicket against Anderson.
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Despite gusts up to 50mph here, England refused to be blown off course as they mastered the tricky conditions to reinforce their credentials as tournament favourites.
Joe Root was the pick of the English batsman with 64, while Liam Plunkett did the damage with the ball picking up 4 wickets for 55.
Adil Rashid found the fence a couple of times before Santner trapped him lbw with one that shot on for 12, leaving Buttler as England's key man. They could not play the full 50 overs as they were all out in 49.3 overs but by then, they have already scored 310 runs.
Hales slapped Milne high over long-off but, for the second match in a row, it was "six and out" for the Nottinghamshire opener after he was bowled next ball by a good-length Milne delivery. Rare moments of ambition on a workmanlike day, but by the time Southee ended England's innings three deliveries early with wickets in successive balls enough to swing the match in England's favour.
"A credit to the way England bowled", Williamson said. Stokes proved a key threat with a knock that included four fours and two sixes before he looped an uppercut nearly straight to Milne at third man off Boult.
The second, in central London on Saturday, happened within a mile of the hotel some England players were using rather than travelling home between matches. He was doing a good job of it, too, before Mark Wood got one to rear alarmingly and it rapped Williamson's gloved thumb. The 26-year-old showed no signs of ankle and calf injury which bothered him in the last game to milk Kiwi bowlers, especially left-arm spinner Mitchell Santer whom he spanked for 29 runs in 22 balls.
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