Kane Williamson was officially and unofficially New Zealand's best batsman on the fourth day of the second Test as his 26th Test century allowed New Zealand to lead England by 257 runs after following on.

Tom Blundell made 90 and was the last man out as New Zealand's second innings ended at 483 less than an hour before stumps on Monday.

Under New Zealand-born coach Brendon McCullum, England have already achieved their highest successful Test run chase, scoring 378 to beat India at Edgbaston last year. This chase for 258 with more than 100 overs available would seem a walk in the park by comparison.

Tim Southee removed Zac Crawley (24) with a ball that cut back to hit off peg and at stumps England were 1-48, needing 210 from 103 overs on the last day to sweep the two-match series.

The odds still heavily favour the visitors but Williamson at least gave New Zealand hope.

When he reached 29 on his way to 132, he became New Zealand's highest run-scorer in Tests, overtaking his former teammate Ross Taylor, who ended his career last year with 7,682 runs.

And in batting for all of the fourth day, in productive partnerships with Henry Nicholls, Daryl Mitchell and Tom Blundell, Williamson guided New Zealand from a 226 run deficit when England enforced the follow-on Sunday to a respectable lead.

"I don't sort of think too much about records," Williamson said. "It's all about the team and the position you're in and trying to do more.

"It was nice to be part of some partnerships today and get a pretty good second innings effort on the board. Having said that you always want more and we were hoping for a few more in terms of the position we got ourselves into. But all to play for tomorrow."

After making only 10 runs in his previous three innings in the series, Williamson showed why he is New Zealand's best batsman when the chips are down. The match was in the balance at the start of the day: New Zealand was 3-202, still 24 runs behind England, who had just taken the second new ball.

Williamson and Nicholls (29) erased the deficit by the ninth over and saw off the new ball in a partnership of 55 for the fourth wicket.

Daryl Mitchell came in when Williamson was 34, and rushed past him to a half century from 52 balls. Williamson then reached his own fifty, from 148 deliveries.

Mitchell was out for 54 in a 75-run partnership with Williamson, when New Zealand's lead was 71. Tom Blundell then provided Williamson the extended support he needed to gradually improve New Zealand's position.

Williamson had batted for seven-and-a-half hours when England gave Harry Brook - primarily a batsman but also officially listed as a medium pacer - his first bowl in Test cricket. He snared the prized wicket, through a faint edge to the keeper.

When Williamson was out, New Zealand's resistance was broken and the end came quickly.