The series win over the World Cup finalists comes less than four months after England exited cricket's showpiece in the group stage.
"We have sort of come out of leftfield with a new-look side, Joe Root, Jos Buttler," England captain Eoin Morgan said.
"Jonny Bairstow was incredible, what was probably our worst batting display of the series, he stuck his hand up and won us the game," he said.
Despite collapsing to 45-5, England reached its revised target of 192 in 26 overs under the Duckworth-Lewis calculation with an over to spare in the rain-affected game at Chester-le-Street in northeast England.
Bairstow was summoned by England only on Friday to replace wicketkeeper Jos Buttler, who split the webbing below his left thumb in practice.
Bairstow proved he can hit as powerfully as England's first-choice wicketkeeper-batsman, and secured only England's second ODI series triumph over New Zealand in 21 years.
After the Kiwis made 283-9, England's reply following a three-hour break between innings thanks to drizzle began miserably against spinner Mitchell Santner.
Brendon McCullum's surprise decision to open with the left-armer paid remarkable dividends and a career-best 3-31, as Alex Hales, Joe Root and Morgan went cheaply.
England's shortened chase was in almost immediate difficulty, but Bairstow took over first in a sixth-wicket stand of 80 in just 57 balls with Sam Billings.
Bairstow stayed the course for a match-winning maiden ODI half-century, albeit being dropped by wicketkeeper Luke Ronchi on 39, and by Santner when he uppercutted Matt Henry to third man on 56.
By the time he and Adil Rashid saw England home, in an unbroken stand of 54, Bairstow had hit 11 fours off 60 balls. It was a fitting climax to the first five-match ODI series ever to produce more than 3,000 runs. England prevailed despite half-centuries for New Zealand from Martin Guptill (67) and Kane Williamson (50), and a late cameo from Ben Wheeler worth 39.

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