The Yorkshireman had been called in as a last-minute replacement for the injured Jos Buttler on Friday and hit 83 not out off 60 balls to see England home under the Duckworth Lewis method by three wickets with six balls remaining after 24 overs were lost to rain.
Bairstow’s Yorkshire team-mate Adil Rashid also enjoyed another day to remember, taking 2-45 from his 10 overs as New Zealand posted a testing total of 283-9 from their 50 overs.
He was then alongside Bairstow at the end of the England innings, contributing 12 in a partnership of 54 which was scored off just 4.5 overs.
After Brendon McCullum’s surprise decision to open with the slow left-armer paid remarkable dividends and a career-best 3-31, 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 one-day international half-century, albeit being dropped by wicketkeeper Luke Ronchi on 39 and then later by Mitchell Santner when he late cut Matt Henry to third man on 56.
It was a fitting climax to the first five-match ODI series ever to contain more than 3,000 runs, England prevailing despite half-centuries from Martin Guptill (67) and Kane Williamson (50) and Ben Wheeler’s late hitting.
Set a revised target of 192 in 26 overs, England’s reply following a three-hour break between innings thanks to stubborn drizzle began miserably against Santner.
First, Alex Hales was brilliantly caught one-handed high to his left by Williamson off Santner, and then Joe Root was stumped by a juggling Ronchi - who collected a painful rebound off his chin in the process.
Eoin Morgan’s prolific run of form came to an abrupt end when he picked out deep midwicket off the young spinner to go for a first-ball duck.
Ben Stokes crunched a catch off Wheeler straight to mid-off, and then opener Jason Roy donated a maiden wicket to debutant Andrew Mathieson with his first ball in international cricket - lobbing a simple catch to point.
Billings and Bairstow took over, until the Kent batsman was caught by a diving Ross Taylor at midwicket - and then David Willey holed out too.
But England, Bairstow especially, would not be denied.
Earlier, Guptill and Williamson’s second-wicket stand of 94 had helped provide New Zealand with a 30-over platform of 150-3 - but thanks to Stokes (3-52), neither remained to cash in during the second half of the Kiwi innings.
Williamson under-edged a front-foot pull on to his stumps, and Guptill went caught-behind to some extra bounce.
After being put in on a cloudy morning, the tourists lost McCullum in the first over.
He had gone up the wicket to Steven Finn and smashed him over long-on for six the previous ball, but was then cramped for room on the back foot and chopped on to his stumps.
New Zealand soon had to reassess possibilities, on a slower pitch than during the rest of the series and under lights throughout.
They were well-served again by the prolific Williamson with his fourth successive 50, only for the regular fall of wickets to prevent momentum.
Rashid bowled impressively and got his reward when the promotion of Santner, to target him again as he had at Trent Bridge, backfired with a leg-break which bowled the advancing left-hander.
Then after Morgan held back Rashid’s final over with the powerplay under way, the leg-spinner returned and spotted Grant Elliott charging at him too - and a flatter googly allowed Bairstow to complete the stumping.
Taylor had escaped a half-chance on 19, a diving Root failing to hold on at short cover off Rashid, and was still threatening to make England pay.
But when he too went three short of his 50, caught-behind off the returning Willey in the 42nd over, New Zealand were struggling to reach par.
Ronchi found mid-off driving at Willey to go too, a third wicket for the addition of only nine runs.
With only the tail left, New Zealand had to grab what they could.
That was to include 22 off the last over from Finn, Wheeler hitting the final three balls for four, six and six - but it was still not enough.