England's bowlers fought back with four wickets after tea to give the home side the advantage after day three of the third Test at Headingley.
New Zealand were 125-1 at tea, leading by 94, and in a position to take charge but Jamie Overton removed Tom Latham (76) with the first ball of the evening session and, following a short rain delay, England struck a further three times to leave the visitors 168-5, leading by 137, when the rain returned to bring the day's play to a premature end.
England had earlier posted 360 to earn a 31-run first-innings lead, with Jonny Bairstow's wonderful innings ended on 162 and Overton coming up agonisingly short in his bid to score a century on debut, dismissed by Trent Boult (4-104) for 97.
Latham and Kane Williamson (48) seemed to have changed the momentum of the game but England's late flurry means the Black Caps are - yet again in this series - relying on Daryl Mitchell (4no) and Tom Blundell (5no) to dig them out of a hole.
Overton falls agonisingly short of a debut century
Bairstow had rightly taken centre stage after reaching a majestic 95-ball century on the second evening but as play began on day three, England resuming on 264-6 having been 55-6, the focus had shifted to junior partner in that remarkable double century stand.
Overton was 11 runs short of a hundred on debut having batted beautifully the previous evening. But there were understandable signs of nerves as he tried to get himself going again.
There were no such issues for Bairstow and he was soon celebrating his 150, from just 144 balls, the second fastest 150 by an England player in Test cricket.
At the other end, Overton was inching ever closer to his milestone and a drive, squeezed past the cover fielder for four off Boult was met with a huge cheer from the Headingley crowd.
The big moment never arrived for Overton, though, as, after playing and missing a number of times, Boult found his edge and Daryl Mitchell pouched the low catch at first slip.
Overton's disappointment was clear and Bairstow ran to console his teammate as he trudged off to a standing ovation, with one last angry swipe of the bat as he stepped over the rope.
An England record 241-run stand for the seventh wicket was over but the home side's fun with the bat continued.
Bairstow and Broad earn England first-innings lead
Bairstow took them to 300 with a boundary thumped through the covers before Stuart Broad delighted the fans by pumping Boult over extra cover for a pair of fours and following it up with a big, straight six.
Neil Wagner was pulled into the stands next over by Broad with England moving past New Zealand's first innings 329 in the last over before drinks.
The innings came to a fairly abrupt end with Broad (42 off 36 balls) bowled by Tim Southee (3-100) and Bairstow, having been dropped by Michael Bracewell on 161, holing out to give the off-spinner his first wicket and bring to an end a fabulous innings.
Jack Leach (8) was then trapped lbw by Southee to wrap up the innings after just 67 overs, with England, from 55-6, having managed to swashbuckle their way to a handy first-innings lead.
There was no chance of a break for Bairstow after his heroics with the bat as he was called upon to keep wicket with Ben Foakes suffering from a stiff back and sent back to the team hotel.
Latham and Williamson build Black Caps lead after lunch
The Black Caps openers got through the five overs to lunch but Will Young fell soon after the break, edging the impressive Matthew Potts to Ollie Pope at third slip with a loose drive.
Williamson came in to join Latham, both players have struggled for runs in the series but with the pitch seemingly starting to flatten out - albeit with the occasional ball doing enough to encourage the bowlers - the experienced duo were soon looking comfortable, the first innings deficit was wiped out and New Zealand set about building a match-winning lead.
Ben Stokes brought himself on to bowl for the first time in the match after 22 overs but struggled for rhythm as he repeatedly fed Latham leg stump half-volleys that the left-hander was only too happy to put away through midwicket.
That allowed Latham to get through to his 23rd Test fifty, and first of the series, from 70 balls and he had progressed to 72 before England next fashioned a chance.
With tea approaching, Broad did what he has done to left-handers so often in recent years from around the wicket. The ball was angled in, nipped away and the edge was found. But on this occasion, the catch was dropped. Joe Root the culprit at first slip.
England hit back in evening session
One down at tea, New Zealand's lead was only just shy of 100 and the opportunity was there for them to seize control of the contest.
Instead, for the umpteenth time in the series, England came roaring back at the World Test Champions.
First ball after tea, Overton had Latham caught behind. The angle in from around the wicket and nip away doing for another left-hander.
The fast bowler backed it up with a sharp bouncer to greet Devon Conway, who was clunked on the helmet.
England were up but before they could make any further inroads, a band of rain came in and although the umpires initially tried to keep play going, it got heavier and a 20-minute delay ensued.
Again, though, the break worked for England with Root (1-7) making up for his earlier drop by dismissing Conway with the first ball after the restart. The left-hander prodded forward, got an inside edge and Pope took a brilliant one-handed catch at short leg.
Root was promptly taken out of the attack and replaced by Potts (2-20). It was an inspired change as the Durham seamer removed the well-set Williamson (48), nibbling the ball away a fraction and extracting a little extra bounce from back of a length to find the edge through to Bairstow.
Headingley had come alive again and Broad, Stokes, Bairstow and Root all did their share of gesturing to the Western Terrace to keep the volume levels high.
The pressure was growing on New Zealand and another savvy bowling change from Stokes brought the next wicket, Henry Nicholls (7) advancing to Leach (1-26) but only managing to chip the ball back to the left-arm spinner for a straightforward return catch.
With the clouds growing ever darker overhead, England were pushing hard to break the partnership that has caused them so much pain in recent weeks but Mitchell and Blundell held firm until the rain returned to bring the day to a close.
Stats of the day
- This is the 229th occasion on which a team has lost its sixth wicket at 55 or fewer. England's 360 is the highest total any team has recovered to, beating the previous record of 284 by Australia against England at Sydney in 1895.
- Aside from Jonny Bairstow, the only other Yorkshire player to score at least 150 in a Test for England at Leeds is Geoffrey Boycott, who scored 246no against India in 1967 and 191 against Australia in 1977. Matthew Elliott, Sachin Tendulkar and Younis Khan all scored 150-plus in Tests here and also represented Yorkshire.
Watch day four of the third LV= Insurance Test between England and New Zealand, at Headingley, live on Sky Sports Cricket with coverage starting at 10.15am and play getting underway at 11am, on Sunday.