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.
Grealish feeling the love from 'top manager' Carsley in England revival
Jack Grealish is feeling the love playing under interim head coach Lee Carsley after the Manchester City midfielder's goal helped England to a 3-1 win over Finland on Sunday.
Grealish was on target in the 18th minute, combining well with Angel Gomes for his fourth international goal, before Trent Alexander-Arnold and Declan Rice sealed the Nations League triumph.
The 29-year-old has now scored two goals in three appearances under Carsley, as many as he did in his first 36 England caps when playing for Gareth Southgate.
Grealish made his feelings known after being left out of England's Euro 2024 squad, and has been a player reborn since his introduction back into the fold.
"We could have had a few more, but it was difficult at times," Grealish told ITV on his team's display in Helsinki.
"Whatever happens with the England manager, people will always say negative stuff.
"Before, people were crying out for all attacking players to play, and it didn't work. I don't get it, it can happen in games.
"I love coming here, a top, top manager and I love playing for him."
Grealish impressed again for the Three Lions, creating more chances (three), having more touches in the opposition box (seven) and accumulating the highest expected goals (xG) tally (0.63) for Carsley's side.
Arsenal's Rice has also found a scoring streak since Carsley's arrival at the helm, notching his fifth international goal after turning home Ollie Watkins' cross late on.
With Rice and Grealish's strikes, it was the first time the same two players have scored in back-to-back England away games since Bukayo Saka and Tammy Abraham did so against Andorra and San Marino in 2021.
Rice was quick to lavish praise on Grealish after his "special" performance at the Helsinki Olympic Stadium, while also lauding Carsley's impact on the squad.
"Do you know how good Jack is? He has something very special," said Rice. He looks really confident, and I am buzzing for him. When he is playing well and happy, he is a massive boost for England.
"Since the manager has come in, he has been so honest, so refreshing. He has a way of playing, and he really wants us to stick with that."
Stokes looking 'great' as England captain prepares for Pakistan return
Ben Stokes is expected to come back into England's side for the second Test against Pakistan, with the all-rounder returning to his peak fitness.
England captain Stokes has been out since the start of August with a hamstring injury but was seen in the nets bowling at full pace ahead of the next Test, which starts on Tuesday in Multan.
Former team-mate and bowling coach James Anderson says Stokes is firing on all cylinders as he prepares to return.
"He looks great. He has worked really hard on his fitness and looking as strong as I've ever seen him," Anderson, England's all-time leading wicket-taker, said to BBC Sport on Sunday.
"He's had a good bowl in the nets and looks good to go."
Anderson acknowledged that managing Stokes' workload could work favourably for England, who will expect spinners Jack Leach and Shoaib Bashar, as well as part-time option Joe Root, to do most of the bowling.
"When we're talking about Ben's workloads and his bowling, it might play into our hands with that, with the spinners potentially playing more of a part," Anderson added.
England did not miss Stokes in the first Test, battling to victory by an innings and 47 runs despite conceding 556 to Pakistan in the first innings last week.
Joe Root's stunning 262, coupled with Harry Brook's remarkable 317, led the fightback before left-armer Leach took 4-30 from just 6.5 overs in Pakistan's final-innings collapse.
Questions remain whether the same pitch will be employed in Multan, where cracks were already showing, instead of a new surface.
"Going off the last game, we did see it go up and down, mainly down, towards the back end," Anderson continued.
"The cracks started opening up. I'm no groundsman, but I don't think you can make cracks go back together that easily, certainly in three days.
"You'd expect it to do something off the cracks and with it being dry and hot again, you'd expect the spinners to play more of a part.
"We don't know what we’re going to get. It could be another pitch, or they have repaired this one really well and it's flat again."
Carsley: England deserve 'world-class coach'
Lee Carsley's ambitions for the permanent England role remain unclear, acknowledging the position "deserves a world-class coach" after Sunday's win in Finland.
The Three Lions responded to Thursday's defeat against Greece with a 3-1 victory in Helsinki as Jack Grealish opened the scoring before second-half goals from Trent Alexander-Arnold and Declan Rice.
That made it three wins in four games for Carsley as the interim England boss since Gareth Southgate left the role following July's Euro 2024 final defeat against Spain.
Thomas Tuchel has emerged in recent times as the frontrunner to take charge of England, and Carsley suggested his side need management from someone who has silverware to their name.
"I've not really thought much about it. I keep saying the same thing. My remit was six games and I'm happy with that. This is a privileged position," Carsley said when asked about his full-time ambitions on ITV.
"I'm really enjoying it but I didn't enjoy the last two days. I'm not used to losing in an England team, I don't take losing well.
"People are always going to try and put their chips on one side. I'm in the middle. My bosses have made it clear what they need from me.
"This job deserves a world-class coach who has won trophies and I am still on the path to that."
England underwhelmed in a 2-1 defeat to Greece on Thursday but Carsley was delighted with the response.
"We were looking for a reaction, that was a big thing," he added. "I think they've shown that they respond well, in the best way. I thought we were a lot better.
"We played a lot more controlled, we had massive possession, created a lot of chances, but I think we can still do better.
"The way they set up, they were well organised. Not a lot of space, we had to create that space, but if you have as much possession as we did then you're always going to get a chance."
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