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.
ECB chief insists no decision made on Mott future
England and Wales Cricket Board chief executive Richard Gould has denied reports a decision has already been made on Matthew Mott's future as white-ball coach.
Mott's future has been called into question in the aftermath of England's failure to defend their T20 World Cup crown in the United States and West Indies, losing to India in the semi-finals.
Mott also oversaw England's calamitous 50-over World Cup campaign last year, as they lost six of their nine matches in India and crashed out in the group stage.
Reports earlier this week suggested the decision had already been made to dispense with Mott's services, with Eoin Morgan a contender to succeed him, though the former limited-overs captain has since said he has no interest in the role.
Asked by BBC Test Match Special if Mott's future had already been decided, Gould said: "That's not true. That's certainly not true.
"Matthew Mott is a really good guy and coach. He's got a great track record and it is the same with [captain] Jos [Buttler].
"We are always assessing options - that is what happens in high-performance sport, you are always assessing your options.
"You never want to be drawn into being given the dreaded vote of confidence or anything like that. Competitive sport always brings scrutiny and decisions.
"We'll constantly want to assess our options but we'll always want to do the right thing by the sport, the team and individuals."
West Indies grab three late wickets on day one as third Test against England in the balance
England lost three wickets in a dramatic end to day one of the third Test against West Indies, leaving them in a precarious position after restricting the tourists for 282.
Gus Atkinson finished with figures of 4-67, while Chris Woakes took 3-69 for England, as only a fine sixth-wicket stand from Jason Holder and Joshua Da Silva saved West Indies from being bowled out for a much lower total.
But England, chasing a 3-0 series whitewash, let their dominant position slip when taking up the bat for the final 35 minutes, Zak Crawley (18), Ben Duckett (3) and Mark Wood (0) being dispatched as bowler Jayden Seales dropped them to 38-3.
Windies skipper Kraigg Brathwaite won the toss and chose to bat, leading his side to a solid start before a spell of three wickets in five overs before lunch put England on top.
Atkinson accounted for Mikyle Louis (26) and Alick Athanaze (2) on either side of Wood sending stumps flying with a full delivery to dismiss Kirk McKenize for 12.
Brathwaite's knock of 61 was brought to a halt shortly after the action resumed, the captain gloving Wood's leg-side ball to Jamie Smith as the tourists slid from 76-0 to 115-5 in 45 balls.
Holder (59) and Da Silva (49) then shared 108 to drag the Windies towards a respectable total, but things looked bleak for them when the latter feathered Woakes' ball through to Smith.
Having gone 30 overs without a wicket, England needed just 14 more to polish off the tail, the highlight being a terrific diving catch from Joe Root to send Gudakesh Motie (8) packing.
England were given just over half an hour with the bat to cap Friday's action, but any hopes of a serene finish were soon dashed.
Holder made two terrific catches off Seales' bowling, the first from Crawley's thick outside edge and the second to dismiss Wood for a duck, either side of Alzarri Joseph's cracking delivery accounting for Duckett.
That spell ensured what had been a good day for the hosts ended on a sour note, with the Windies sure to target quick wickets when the action resumes on Saturday.
Data Debrief: Atkinson and Seales dominate
This series began with all the focus on James Anderson as England's greatest-ever bowler bowed out at Lord's, but Atkinson has taken centre-stage since making his Test debut in the opening match and now has 20 wickets through five innings.
That is eight more than West Indies' Jayden Seales, the next-most prolific bowler in this series, has managed.
Seales was determined to have an impact on day one, though, and his two wickets at the death have set the stage for a far more competitive match than those England won at Lord's and Trent Bridge.
McAllister cannot see Klopp or Guardiola succeeding Southgate
Gary McAllister finds it hard to believe that either Jurgen Klopp or Pep Guardiola will succeed Gareth Southgate as England manager.
Southgate, who led England to back-to-back European Championship finals, ended his eight-year tenure following their defeat to Spain in the Euro 2024 showpiece.
The 53-year-old was often accused of a cautious approach despite only Walter Winterbottom (383) and Alf Ramsey (224) overseeing more England goals than his 213, with supporters wanting to see a more attack-minded manager take over.
And two of the names linked with the vacant position have been pioneers of Premier League football in recent years.
Klopp ended his nine-year stay at Liverpool in May to take a break from management, while some expect Guardiola to leave Manchester City at the end of his current deal, which expires next year.
The pair have won 653 games between them and shared 25 major honours during their time in England and could be seen as the ideal candidates to end the Three Lions' 58-year wait for silverware.
However, former Liverpool and Scotland midfielder McAllister believes Klopp and Guardiola are unlikely to become England's next manager.
McAllister, who played 57 times for his nation, believes supporters would prefer an English manager at the helm.
"I think people are linking Jurgen with the England job purely because he has experience working in the English Premier League," McAllister told Stats Perform.
"He's worked with elite players for many years now at Dortmund and at Liverpool. So people are putting two and two together.
"Personally, I don't see it happening and I think I also see that there were links to Pep Guardiola and I don't see Pep managing England either.
"It's hard for me to comment on this because I'm obviously not English, I'm Scottish.
"The people I speak to within the game, there is a feeling that the manager of England should come from St George's Park, which is the headquarters of English football, the FA and all the coaching programmes that they have there.
"Why would you have all this and then put a manager not from England in? I think most of the people in England are looking for an English manager."
The Three Lions' next game is a Nations League clash with the Republic of Ireland in September, with Finland their next opponents three days later.
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