Despite Kane Williamson's best efforts, the Blackcaps are staring at defeat and a series sweep against England, heading into the final day at Wellington.
On a day that already saw him pass Ross Taylor's tally for the most test runs by a New Zealander, Williamson went on to post a record-extending 26th test century, taking the home team into the lead at the Basin Reserve.
But half-centuries to Daryl Mitchell and Tom Blundell aside, the rest of the Blackcaps order struggled to build on Williamson's efforts, bowled out for 483 after tea, setting England 258 runs for victory in more than three sessions.
Captain Tim Southee struck with the ball, as England reached 48/1 at stumps, needing another 210 for victory on the last day.
Defeat would end the Blackcaps' unbeaten home test series run, which began in 2017.
Returning to the crease for day four on 25, Williamson batted to reach three figures from 226 balls, with eight boundaries.
The former captain added half-century stands with Henry Nicholls (29) and Daryl Mitchell (54) en route to his ton, but found an invaluable ally in Tom Blundell, as the pair put on 158 for the sixth wicket.
After being asked to follow-on on Sunday, Williamson, along with openers Tom Latham and Devon Conway, forced England to bat again with a fourth innings chase for victory.
His vigil was ended by an unlikely hero for England, when he was strangled down legside by part-time bowler Harry Brook for 132 from 282 balls, but more importantly, putting the Blackcaps ahead by 229 runs.
At the other end, Blundell batted on without any real support from his batting partners. After he was dropped by James Anderson on 30, the wicketkeeper went on to reach 50 from 80 balls, adding to his career-best 138 in the series' opening test at Mt Maunganui.
Wickets falling at the other end severely hurt the chances of pushing for victory on day five, as New Zealand lost 5/28 to allow England back into the game.
Michael Bracewell was run out in farcical fashion for eight, after not grounding his bat, while Southee couldn't repeat his first-innings heroics, when he hacked Jack Leach to substitute fielder Matt Potts at point.
Matt Henry came and went for a three-ball duck, as he edged Leach to Joe Root at slip, leaving the Blackcaps nine down, slipping from 455/5 at the time of Williamson's dismissal to 482/9, when Neil Wagner joined Blundell.
Forced to take risks, Blundell was the final batter to fall, when he edged to Root at slip for 90, giving Leach a five-wicket haul as reward for nearly 62 overs of bowling.
In reply, England opener Zak Crawley survived a runout chance, as Conway missed the stumps at the striker's end, but was bowled by Southee for 24 to leave the tourists 39/1.
Ben Duckett (23 not out) and nightwatchman Ollie Robinson batted to the end of play without further loss, and will resume on the final day in the push for victory.
The Blackcaps are currently winless from their last seven tests, including five losses and two draws. Under the leadership duo of captain Ben Stokes and coach Brendon McCullum, England have won 10 of their last 11 and - ominously - haven't lost when chasing, batting last in six of those victories.
England 435/8 declared (Brook 186, Root 153 not out; Henry 4/100) & 48/1 (Crawley 24, Duckett 23 not out; Southee 1/19)
New Zealand 209 (Southee 73; Broad 4.61) & 483 (Williamson 132, Blundell 90; Leach 5/157)
England need 210 runs for victory with nine wickets in hand
