Both Jonny Bairstow (138) and Joe Root (102) hit superb centuries.
The Black Caps need to win tomorrow to keep the five match series alive and Radio Sport will have live commentary on air and online from 10.30am tomorrow.
In the end it was Grandhomme (23) and Nicholls (13) who helped and an injured Taylor, who was declared man of the match, to take their side home.
Ross Taylor struck his career best ODI score with an unbeaten 181.More news: Trump says he'll counteract any Russian Federation meddling in midterms
Following the massive target, New Zealand lost two early wickets in the form of openers Martin Guptill and Colin Munro at the score of two.
Taylor took his 181 runs from 147 balls with 17 fours and six sixes, gradually making the impossible look possible. He hit Chris Woakes for a six and a four in the next over and the game was as good as done.
England seemed to have reached match point.
But he also found scoring hard as Williamson, back after missing a match with a hamstring strain, used his slower bowlers well through the middle of the innings.
Bairstow clubbed some absolutely massive sixes.
With three runs needed off the final over, Nicholls faced two dot balls then smashed Tom Curran for six as a tearful Taylor left the field to a standing ovation.More news: Germany to finally have a new gov't as SPD agrees in referendum
But Santner was culpable when he put down an easier chance at extra-cover off Trent Boult to reprieve Bairstow on 74.
Root himself was dismissed the over after going through to his 11th ODI century, and England were thankful for a flurry of boundaries from Tom Curran (22no) in the final over to take their total up to 335. However, it heralded an epic England collapse, with the next seven wickets falling for 38 runs.
59- Runs scored by England in the last ten overs for the loss of five wickets. Kane Williamson leads the way at 8/1, in the wake of his brilliant but futile hundred at Wellington, with Joe Root second favourite at 17/2.
The matches can also be watched on SKY Sport NZ in New Zealand; all matches live streamed on the Sky Go.
This former New Zealand captain used to be a six-hitting machine for almost half of his career before he changed his game.
"An outstanding performance from him and a great partnership with Tom".More news: Attackers try to saw off South African athlete's legs
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