England rejected talk their New Zealand series was over when they ended day two on Sunday at 39 for two, but accepted it would need a special performance to turn their fortunes around in Hamilton.
New Zealand, meanwhile, ruled out thoughts of playing for a draw as they targeted a clean sweep in the two Test series after a comprehensive innings victory in the first match.
With BJ Watling, the architect of the first Test win, again holding the innings together New Zealand recovered from 191 for five to reach 375 in their first innings in Hamilton with Watling and debutant Daryl Mitchell featuring in a 124-run stand for the sixth wicket.
England, in 18 overs before stumps, lost Dom Sibley and Joe Denly cheaply while Rory Burns was dropped twice to be not out 24 with Joe Root on six.
Stuart Broad, England's chief wicket taker with four for 73, said there was little in the pitch to assist the bowlers and two good centuries should be enough to set them up for a series-levelling win.
"The opportunity is there to go and bat big once," he said.
"There's not a huge amount of pressure, not a lot happening with the pitch, not a big scoreboard pressure, there's a chance for a couple of people to go and get hundreds ... and leave ourselves a day to bowl them out.
Mitchell, who scored 73 on debut, said New Zealand's mindset was not to play for a draw.
"Every Test you're aiming to win so we're trying to find a way to win this Test match," he said
"It's a nice wicket to bat on at the moment, but there's some things there we can try to exploit later on."
England made a confident start to day two when they removed both overnight batsmen early but then lost the initiative as Watling and Mitchell staged their repair mission before Broad removed both batsmen either side of the tea break.
Watling was out for 55 on the last ball before the interval while Mitchell departed in the fourth over after play resumed.
New Zealand's last four wickets added a further 60 runs, with Broad finishing with figures of four for 73 and Chris Woakes three for 83.
All-rounder Mitchell, the son of former All Blacks coach and now England assistant rugby coach John Mitchell, was unruffled in his maiden Test performance.
He brought up his 50 pulling Ben Stokes through mid-wicket for four in a 159-ball innings which included eight boundaries and one six.
An even more cautious Watling, who reached his 18th half century with an elegant cut to the cover boundary off Sam Curran, faced 192 deliveries for his 55.
It was slow going by the pair, but from New Zealand's viewpoint their innings lasted almost two days which left England with only a remote chance of winning the Test to square the series.
England had their tails up at the start of the day when overnight centurion Tom Latham added only one boundary to his total before he misjudged a Broad delivery seaming back at him and was bowled for 105.
Broad stayed in the action to catch Henry Nicholls for 16 off Sam Curran, which brought the untested Mitchell to the middle to join Watling and bat New Zealand to a position of strength.