New Zealand 209 (Southee 73, Broad 4-61) and 202 for 3 (Latham 83, Conway 61) trail England 435 for 8 dec (Brook 186, Root 153*, Henry 4-100) by 24 runs
Wellington: England have work to do in order to win the second Test after New Zealand's defiance following-on in Wellington.
The home side ended day three on 202-3, 24 behind after beginning their second innings 226 adrift.
Tom Latham made 83 and Devon Conway 61 in an opening stand of 149, before New Zealand lost three wickets for 18 runs to the spin of Jack Leach and Joe Root.
But Kane Williamson and Henry Nicholls dug in, at times painstakingly so. Williamson crawled to 25 not out from 81 balls, Nicholls 18 from 70 in an unbroken partnership of 35.
Captain Tim Southee earlier clubbed 73 from 49 balls to drag the Black Caps to 209 all out in their first innings.
Southee added 98 for the eighth wicket with Tom Blundell, only for both to fall to Stuart Broad as part of his 4-61.
Then came the New Zealand rearguard, leaving a match that could have been one-sided delicately poised.
A decision made by a captain to enforce a follow-on or declare (which England did in their innings) is only ever judged in hindsight.
When Ben Stokes opted to use the follow-on, the first time he has had the opportunity under his captaincy and the first enforced by England since August 2020, it was incredibly hard to argue.
Faced with such a huge deficit, left-handed openers Latham and Conway gradually chipped away at England's advantage with old-fashioned Test values: patience, determination and sound judgement.
Both men left well. Latham was strong off the pads, Conway drove handsomely through the covers and also hit Leach for six over long-on.
An incredibly sharp chance back to Leach off Latham was the closest England came until Ollie Pope once again showed his value as a close fielder by holding on to Conway's inside edge.
Three overs later, Latham missed a sweep to be lbw to Root and when Leach produced a ripper that turned past Will Young's defensive stroke, New Zealand were three down still 59 adrift.
But Williamson and Nicholls dropped anchor with dead-batted defence. Nicholls survived an inside edge flashing past Pope at short leg when he had eight.
The brief burst with the second new ball could not part them and New Zealand have the likes Daryl Mitchell, Blundell, Michael Bracewell and Southee still to come on Monday.
England might have been hoping for victory inside three days when play resumed with New Zealand 138-7, 237 behind.
On a grey morning, Southee caused chaos. From 23 not out, he swiped 50 from the 30 balls he faced until his dismissal. Three sixes were belted off a single Leach over, another maximum pulled off Ollie Robinson.
He was put down by Leach, a skier at fine leg, but next ball chipped Broad to Zak Crawley at mid-wicket.
In Broad's next over, Tom Blundell hammered to mid-on and was out for 38, then Matt Henry looped a short ball to point.
After bowling only 11.2 overs, England invited the Black Caps to bat again, only to encounter some hard toil in the warmest weather of the match.
England's pace bowlers got the ball to swing, but bowled a touch too wide to utilise the assistance. There was turn for the spinners, albeit with Leach erring on the short side.
Stokes held himself back until the 50th over and sent down two overs of ineffective bouncers, including a wide and three no-balls, before Leach found the breakthrough.