England require another 210 runs for victory with nine wickets in hand after the history-making Kane Williamson set up a thrilling fifth-day finale with his 26th Test century in Wellington on Monday.
Williamson became New Zealand's all-time leading Test run scorer on his way to 132 as the Black Caps posted 483 in their second innings to set England a target of 258 for victory in the second Test.
The hosts potentially could have set England a target beyond 300 if not for spinner Jack Leach cleaning up the tail in quick time, finishing with 5-157, as New Zealand lost their final four wickets for five runs.
After Zak Crawley survived a Devon Conway run-out chance, Tim Southee removed the opener by jagging one back to take the top of off-stump as England reached stumps at 48-1 from 11 overs, with Ben Duckett (23 not out) and night watchman Ollie Robinson (1 not out) at the crease.
Victory is on the table for either side, with New Zealand roaring back into the contest as they look for a series-levelling win to preserve their record of not losing a home Test series since 2017.
The hosts resumed at 202-3, trailing by 24 runs, and lost Henry Nicholls for 29 to Ollie Robinson before they had got ahead of the ledger. Daryl Mitchell fell to Stuart Broad for a run-a-ball 54 before Williamson took charge alongside Tom Blundell in a 158-run stand which ensured the hosts a shot at victory.
The second session belonged to Williamson and Blundell who batted through, with the former skipper reaching triple figures before tea, while James Anderson dropped the latter.
Williamson eventually departed for 132 from 282 deliveries when Ben Stokes' hopeful review revealed he had tickled a leg-side delivery from Harry Brook, bowling at Test level for the first time, to wicketkeeper Ben Foakes.
Foakes' quick thinking led to Michael Bracewell's inexplicable run out before the Black Caps' tail fell meekly searching for fast runs, eager for a crack at England's top order late in the day's play.
Run-chase experts
England have won 10 of their last 11 Tests with fourth-inning run chases and are unlikely to be fazed by the target, despite history suggesting otherwise. The tourists started positively despite their awkward 11-over stay in the final session, erasing almost 20 per cent of the target already.
Black Caps in the game
On the flip side, New Zealand are in with a shot at a remarkable victory. Only three teams in Test history have previously won a game after being made to follow-on.