England need 210 more runs to win the second Test after finally dismissing New Zealand for 483 on day four in Wellington.
Kane Williamson made a faultless 132 and Tom Blundell 90 as the Black Caps ground their way back into the game after being asked to follow-on.
It left England needing to pull off the highest run-chase by any team that has enforced the follow-on in a Test, while only three other teams have ever made more than New Zealand following-on against England.
The toil of England’s bowlers on a docile pitch was made harder by captain Ben Stokes not joining the attack because of his troublesome left knee.
Even Harry Brook was called on to bowl his medium pace, remarkably claiming Williamson as his first Test wicket and sparking a New Zealand collapse of 5-28.
Left-arm spinner Jack Leach took the final three wickets to fall to end with 5-157.
England were left with 11 overs to bat at the end of the day, in which time the under-pressure Zak Crawley was bowled through the gate by Tim Southee for a skittish 24.
Ben Duckett remains on 23 in the company of nightwatchman Ollie Robinson on one, with England 48-1.