England's Eoin Morgan celebrates his century during the fourth one day international (ODI) cricket match between England and New Zealand at Trent Bridge cricket ground in Nottingham, central England, on June 17, 2015. PHOTO: AFP
Morgan made 113 and Joe Root 106 not out as England finished on 350 for three with six overs to spare.
It was the equal fourth highest total by any team batting second to win an ODI.
Root and Morgan's stand of 198 was the highest third wicket ODI partnership against New Zealand.
England had earlier held New Zealand to 349 for seven in this day/night fixture.
Kane Williamson top-scored with 90 following his 118 in World Cup finalists New Zealand's three-wicket win at Southampton on Sunday.
The most England had previously made batting second to win an ODI was 306 for five against Pakistan at Karachi in 2000.
But they stayed true to their intention to play an attacking brand of cricket following a humiliating first-round exit at this year's World Cup -- which included an eight-wicket defeat by New Zealand.
"It's certainly up there as one of the best games of cricket I've ever played in," said Morgan.
"We thought their score was 25 over par but we played out of our skins."
New Zealand captain Brendon McCullum, who won the toss, said his side had been outclassed.
"It was incredible. At halfway, with 350 on the board we knew they would have to play well to beat us but they blew us off the park," he said.
England scored 97 runs in the first 10 overs of their reply after the innings started with a maiden from left-arm paceman Ben Wheeler.
But Wheeler's next three overs cost 41 runs.
Following a brief rain break, Alex Hales carried on from where he had left with Mitchell McClenagan's first over going for 22.
It culminated in two huge sixes from Nottinghamshire opener Hales, to the delight of his home crowd.
But fast bowler Matt Henry removed Hales (67) and Jason Roy (38) in a spell of two wickets for seven runs in eight balls.
Root came in at 111 for two.
The Yorkshireman was missed on nine, as not for the first time this series, Ross Taylor dropped a slip catch.
Meanwhile former Ireland international Morgan took only 39 balls for his fifty against an attack missing the steadying influence of injured left-arm paceman Trent Boult.
Left-hander Morgan had a lucky break on 66 when he skyed Henry towards deep midwicket, where neither Grant Elliott nor Wheeler -- who almost collided with one another -- got a hand to the ball.
Morgan went to his century in style, with a fifth six, over long-on off Henry. His 73-ball ton also included 11 fours.
He eventually holed out off Southee.
Root posted his second century of the series, following his 104 in England's 210-run win in the first ODI at Edgbaston, in 94 balls, before sealing an emphatic victory by pulling Mitchell Santner's left-arm spin for four.
Earlier, either side of Williamson's innings, New Zealand opener Martin Guptill made 53 and all-rounder Elliott an unbeaten 55 off 52 balls.
The Black Caps, after winning the toss, had threatened a huge score at 187 for two off 30 overs.
But England fought back well with the ball, thanks mainly to fast bowlers Mark Wood (one for 49 in 10 overs) and Steven Finn (one for 51 in 10).
Williamson and Taylor, who made 110 at the Rose Bowl, had shared a stand of 206 on Sunday.
They managed 101 between them on Wednesday with Taylor, lbw to Finn for 42.
Williamson fell when he drove left-armer David Willey to a leaping Adil Rashid at mid-on.
He faced just 70 balls, including 12 fours and a six.
This match was veteran Australian umpire Steve Davis's last in the middle before retirement -- although he will be the replay official for Saturday's series-decider in Durham.
"I thought I was going OK until Brendon asked me to lead the players off (the field)," said Davis. "Then I got emotional.
"It's been great to have the respect of the players."
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