wickets remaining and 104 balls to spare.
Bairstow, who scored 138 in the fourth game in Dunedin, smashed a 58-ball century with eight boundaries and six sixes as he combined with Alex Hales (61) in a 155-run opening stand in ideal batting conditions.
After a see-saw series, both teams enter today's decider with all to play for, with the scores locked at 2-2 following New Zealand's incredible run chase in Dunedin, thanks mostly to Ross Taylor's incredible 181 not out.
Hales, back in place of the injured Jason Roy for his first match of the series and since he announced his white-ball-only future, was no slouch either and passed 2,000 ODI runs for his trouble.
The 34-year-old produced a match-winning unbeaten 181 in the fourth one-day worldwide on Wednesday, despite having aggravated a thigh injury and suffering cramps that restricted his movement and forced him to limp singles in the successful run chase. Woakes and Rashid ripped through their line-up as they scalped three wickets each with the other bowlers chipping in nicely and supporting them.
Bairstow dominated the bowlers, smashing nine fours and six sixes as he thrashed a century from just 58 balls.
After the first four ODIs, which had the series level at 2-2, England had the New Zealand batsmen well worked out.
Once opener Martin Guptill fell for 47, New Zealand looked close to subsiding.
Blackcaps batsman Colin Munro.
They had fortunate escapes with record fourth-wicket partnerships between Ross Taylor and Tom Latham in the victories at Hamilton and Dunedin.
For now, the focus will switch to red-ball cricket as New Zealand prepare to face England in a two-match Test series at home.
That would be Curran's only involvement till the 40th over, by which point New Zealand had turned around their position to 151 for six. Nicholls hit Root's off-spin for six but he top-edged Tom Curran to short leg at an inopportune moment. However, he goes at a wider one next ball, lucky not to be caught at cover.
Nicholls struck an intelligent 55 from 81 balls, while Santner top-scored with a crucial 67 off 71 before he was dismissed early in the second-last over.
Former New Zealand captain Jeremy Coney on Test Match Special: "New Zealand's middle order looked to me as though they didn't know how to defend spin bowling, let alone attack it. Chapman's dismissal was very bad. It was a brilliant innings by Jonny - hitting the ball cleanly like he has all series". His experience, ability to bat long periods on hard surfaces and reputation for digging New Zealand out of trouble with the bat, should see him preferred over Blundell against a quality English attack. In the match England won the toss and let Black Caps to bat first. Joe Root (23 not out) and Ben Stokes, who hit a six to win the game and finish 26 not out, guided England to 229 for three in 32.4 overs. That's something I'm really trying to set my marker out to do.