New Zealand beat England by just one run in a second-Test thriller on Tuesday to draw the series in the most dramatic fashion in Wellington.

The hosts made a slice of history in becoming only the fourth team in 146 years of Test cricket to win after being asked to follow on.

Neil Wagner took the decisive wicket of James Anderson when New Zealand wicketkeeper Tom Blundell pulled off a diving catch at the Basin Reserve to seal a memorable, nail-biting triumph.

The home side had fought back to set an attacking England a target of 258 runs to win, but the visitors were all out for 256 as a gripping two-Test series finished 1-1.

It was only the second time in Test cricket that a side has won by one run, matching the West Indies team who beat Australia by the same wafer-thin margin at Adelaide in 1993. 

"Amazing achievement, hats off to everyone, everyone kept fighting," said left-arm pace bowler Wagner, who finished with 4-62 including the key wickets of Ben Stokes and Joe Root. 

England skipper Stokes was disappointed to have lost, as the attacking "Bazball" cricket under head coach Brendon McCullum hit the buffers, but happy to have played his part in the drama.

"That game is what Test cricket is about -- the emotions we were going through and the Kiwi boys as well," said Stokes, who was born in New Zealand.

"Everyone's got their money's worth today.

"What a game. After I got out, I went to watch and what unfolded was massively up and down," added Stokes.

"It was crazy."

It was the first time New Zealand have won after being forced to follow on. England had managed it twice, against Australia in 1894 and 1981, while India beat Australia in 2001.

A topsy-turvy Test match had swung back to New Zealand during the final two days.

Captain Tim Southee praised the visitors' contribution to a pulsating Test match that will live long in the memory.

"What England have done for Test cricket over the last year or so has been amazing," said Southee, after New Zealand halted England's run of six straight wins.

"I don't know why there always seems to be such close encounters between us, but these games bring out the best in both sides.

"We just never gave up, it was about hanging in there and trusting we would do it."

England won the first Test by a resounding 267 runs and were on course for another victory after declaring their first innings on 435-8, then bowling out New Zealand for 209.

But former skipper Kane Williamson dragged New Zealand back into the Test with a superb 132 in their second-innings 483, leaving England 258 to win.

Having resumed at 48-1, England wobbled on Tuesday morning by losing four wickets for just 27 runs before Root steadied the ship by steering his team to 168-5 at lunch.

As England chipped away at their target, Root's vital partnership with Stokes ended on 121 when England's captain was caught at square leg off Wagner.

The pressure on England intensified dramatically after Root went for 95, also to a Wagner short ball, with England still 57 runs short.

Wicketkeeper Ben Foakes kept England in the fight with a cavalier 35, surviving a dropped catch by Michael Bracewell before clubbing three fours to the boundary.

But just when it looked like Foakes might bring England heroically home, he was caught by key man Wagner in the deep off Southee.

That left last pair Anderson and Jack Leach still needing seven runs for victory -- and the tension went up another notch.

Anderson clubbed a four to get within two runs, before Wagner and Blundell combined to land the knockout punch.

Stokes, who will now turn his focus towards the Ashes and Australia this summer, said it had still been a successful winter, having won 3-0 in Pakistan.

"Disappointing to end on a loss, but four (wins) out of five away from home is something we will take great pride in," he said.

"A few months off and get back to what we love doing."