New Zealand teammates celebrate the wicket of England's James Anderson for their win by 1 run on day 5 of their cricket test match in Wellington, New Zealand, on Tuesday. AP

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.

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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.

England's captain Ben Stokes (left) and his New Zealand counterpart Tim Southee share the trophy on Tuesday. AP

"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.

England's James Anderson (left) and Jack Leach leave the field in Wellington, New Zealand, on Tuesday. AP

"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."

Agence France-Presse