Jonny Bairstow became the first Englishman to score back-to-back hundreds in a World Cup before New Zealand pulled things back to limit the hosts to 305 for eight here on Wednesday.
Bairstow, who had smashed 111 against India in England's previous contest, hammered 106 off 99 balls to lay a solid platform in the must-win game.
Openers Jason Roy (60 off 61) and Bairstow were in punishing mood for the second game in succession, sharing an entertaining 123-run stand after England opted to bat. Bairstow hit as many 15 fours and a six in his knock.
With England cruising at 194 for one in the 31st over, it seemed the home team would bat New Zealand out of the game.
But, with the wicket getting slower as the innings progressed, New Zealand fought their way back into the game on the back of some tight bowling.
Trent Boult (2/56) was impressive again and removed Joe Root (24) just at the right time to trigger a mini collapse that also led to the fall of centurion Bairstow and the dangerous Jos Buttler (11), leaving England at 214 for four.
Spinner Mitchell Santer, who had opened the bowling, then removed the in-form Ben Stokes (11) to make it 248 for five.
The onus, then, was on captain Eoin Morgan to come up with late fireworks, but he too perished after scoring 42 off 40 balls.
Adil Rashid (16 off 12) and Liam Plunkett (15 not out off 12) picked up a few much-needed boundaries to take their team past 300.
Matt Henry (2/54) and James Neesham (2/41), too, put up an impressive bowling performance for New Zealand.
New Zealand were dealt a blow before the start of the game, with pacer Lockie Ferguson being ruled out due to a hamstring injury. Tim Southee, playing his first game of the tournament, leaked 70 runs in nine overs.
The winner of the game qualifies for the semifinals.
For the record, England have never beaten New Zealand in a World Cup game since 1983.
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