New Zealand, set 192 for victory, collapsed to 135 all out as they lost their last five wickets for four runs in 12 balls.
For England, it was the ideal way to sign off ahead of the Ashes after they had shared the two Test series 1-1 and defeated New Zealand, who humiliated them en route to the World Cup final, 3-2 in a thrilling one-day international series.
The first Test against Australia starts in Cardiff on July 8.
Tuesday saw left-arm paceman David Willey (three for 22) and fast bowler Mark Wood (three for 26) mark their England debuts at this level in style.
England's Joe Root was named man-of-the-match for his 68 in the hosts' 191 for seven.
"This felt a million miles away after the World Cup," said England white-ball captain Eoin Morgan.
"Now we have won this game and the ODI series, it reinforces to the guys that, it might not always come off, but we can beat the best in the world in any game of cricket."
New Zealand were 101 for five at the half-way stage but then collapsed in spectacular fashion as England won with 22 balls to spare.
- 'Amateurish batting' -
========================
"I thought that 190-odd was about par. I was not unhappy at half-time, but we batted a bit amateurishly to be honest," said New Zealand captain Brendon McCullum.
"Credit to England, we wish them all the best for what is to come."
New Zealand's Kane Williamson top-scored for the Black Caps with a typically elegant 57 but his side's hopes of victory effectively ended in a 15th over where they lost three wickets.
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