New Zealand captain Tim Southee hailed his team for becoming only the fourth side to win a Test after being asked to follow-on, while conceding fortune played a part in their incredible one-run victory over England.

New Zealand thwarted England's 258-run chase by the slimmest of margins on day five at the Basin Reserve on Tuesday to leave the series drawn 1-1.

Southee said the match was up there with one of the biggest highlights of his career of 92 Tests.

"It's hard to go past being only the fourth Test team to win a Test match having been asked to follow on," the 34-year-old paceman told reporters.

"The guys just taking it in their stride and giving it a shot in the last three days and managing to come out on top, that's, I'd imagine, would be a Test match that will be talked about for a long time.

"(For them) to show that character over the last three days has been very pleasing to see and just an awesome game of cricket to be a part of."

New Zealand had plenty of heroes, with Kane Williamson Man of the Match for his third innings 132 which helped the Black Caps put on 483 after England captain Ben Stokes enforced the follow-on.

Paceman Neil Wagner had four victims in the fourth innings, including the winning wicket when he had tailender James Anderson caught down the legside.

Wicketkeeper Tom Blundell dived to his right to take the Anderson catch, capping a terrific series with scores of 38 and 90 in Wellington and 138 in the first Test loss in Mount Maunganui.

"We got a little bit of luck there with a little flick of a bat down the legside," said Southee.

"Tommy Blundell just capped off what has been not just been a great series, but a great 18 months for him as well."