New Zealand's Tom Latham hit his highest score of the series as the tourists responded after an astonishing England stand featuring Jonny Bairstow's latest hundred and Jamie Overton's 97 on debut in the third Test at Headingley.
World Test champions New Zealand were 125-1 in their second innings, a lead of 94 runs, at tea on Saturday's third day. Latham was 76 not out, far exceeding his previous best of 26 this series, with New Zealand captain Kane Williamson unbeaten on 37.
But with England previously having chased down 299 inside a day to win the second Test and go 2-0 up in the three-match series, there was still plenty of work left for the Black Caps' batsmen. Earlier, Overton fell agonisingly short of a hundred in his first international innings but local hero Bairstow extended his overnight 130 not out to 162.
The pair had come together with the hosts in dire straits at 55-6 but their England record seventh-wicket stand of 241 was the cornerstone of an eventual total of 360 -- a first-innings lead of 31.
Overton, selected as a fast bowler in place of the injured James Anderson, was within one shot of getting to three figures in his maiden international innings when he nicked Trent Boult low to first slip Daryl Mitchell.
The 28-year-old, who resumed on 89, never regained the fluency he had on Friday and it was no surprise when Boult, who had removed all of England's top three with a superb display of new-ball bowling, located Overton's outside edge.
England's new leadership duo of captain Ben Stokes and coach Brendon McCullum had urged the team to play with freedom after taking charge of a side that had won just one out of 17 Tests prior to this series.