Bairstow, who scored a match-winning 111 against India in Edgbaston on Sunday, cracked 106 off 99 balls (15×4, 1×6) as Jason Roy also struck his second fifty in a row by scoring 60 off 61 balls (8×4). England posted 305/8 in 50 overs after electing to bat first.
Bairstow became the first-ever English player to score two back-to-back hundreds in World Cups. It was also his third successive in ODIs against New Zealand.
Chasing 306 for victory, New Zealand gave a poor account of themselves, losing wickets at regular intervals and never really posing any threat. For the Kiwis, who were 186 all out in 45 overs, wicket-keeper-batsman Tom Latham top scored with 57 off 65 balls (5×4). Mark Wood (3/34) returned with best figures for England.
England finished their league engagements in third place on 12 points while New Zealand were pushed down to fourth with 11 points from their full quota of nine games. While fifth-place Pakistan do still have a chance, they would have to beat Bangladesh by a massive margin to come even close to the Kiwis” net run rate.
The Black Caps were reduced to 14/2 after openers Henry Nicolls (0) and Martin Guptill (8) were dimissed inside the first six overs. Nicolls was trapped in front by Chris Woakes (1/44) while Guptill was caught behind by Jos Buttler off Jofra Archer (1/17).
The mainstays of their batting, Ross Taylor and Kane Williamson were then in the middle and just when they were looking good, their skipper was run out in the most unfortunate manner as Wood got his fingertips to a shot by Taylor down the pitch with replays showing Williamson (27) out of his crease.
Once their 47-run third wicket association was broken with Taylor (28) also getting run out, the match swung in England”s favour with the asking rate climbing up every over.
All-rounder James Neesham (19) and Latham shared a 54-run fifth wicket partnership which kept their fading hopes alive. But once Neesham chopped a Wood back of a length delivery on to his stumps, it was all over even as Latham scored his scored his first fifty of the tournament.
Earlier, New Zealand bowlers did well to brave England”s early onslaught and restrict them to below 330 which looked easily achievable at one stage.
After the opening stand of 123 between Bairstow and Roy was broken, New Zealand pacers led by Trent Boult (2/56), Matt Henry (2/54) and Neesham (2/41) put the breaks on by taking regular wickets as England limped to a 300-plus score riding Adil Rashid”s 16 off 12 balls and Liam Plunkett”s 15 off 12 deliveries not out.
England got off to a flying start with dashing Roy and Bairstow in their usual devastating self.
Kiwis started with Mitchell Santner first up but the ploy did not work as the first ball went for four byes and then Roy hit him for a boundary to take nine off the over.
There was no stopping the pair from then on as they took the pacers to the cleaners and forced skipper Kane Williamson to bring in Colin de Grandhomme and Neesham to take the pace off the ball.
New Zealand missed their leading pacer Lockie Ferguson badly after he was ruled out owing to a hamstring niggle, opening the door for Tim Southee who had a forgettable start, being slapped for three back-to-back fours by Bairstow.
Roy brought up his 17th international fifty in 55 balls and a second successive one while Bairstow got to his half century in 46 deliveries.
The pair added 123 runs for the opening wicket before Roy was caught by Santner off Neesham at short cover.
It was only the 19th over and England were 123/1, looking good for another big total.
Bairstow and Joe Root then joined hands for a 71-run first wicket partnership.
Bairstow brought up his 100 in 95 balls, but things started to fall apart for the hosts in the 31st over when Root (24) was caught behind by stumper Latham off Boult.
Skipper Eoin Morgan scored 42 off 40 balls (5×4) but lacked support at the other end.
Bairstow dragged a Henry delivery onto his stumps in the next over and Buttler, sent in ahead of Ben Stokes, failed to make a mark, caught at mid off by Williamson off Boult at 11 as Stokes too played an uncharacteristic knock of 11 off 27 balls before getting out.
Chris Woakes (4) followed suit and the Kiwis firmly reined in England.
Brief scores: England 305/8 in 50 overs (Jonny Bairstow 106, Jason Roy 60; Jimmy Neesham 2/41) vs New Zealand 186 all out in 45 overs (Tom Latham 57, Mark Wood (3/34)