Jamie Overton fell agonisingly short of a debut century in the third Test on Saturday but England still led New Zealand after the first innings.
Overton was out for 97 but Jonny Bairstow extended his overnight 130 not out to 162 on his Headingley home ground.
England, already 2-0 up in this three-match series, were bowled out for 360 in reply to New Zealand’s 329 on the third day — a lead of 31 runs.
It represented a remarkable recovery after they had collapsed to 55-6, with Bairstow and Overton sharing an England seventh-wicket record stand of 241.
“Jonny’s hundred last week would have been special for him, to win the game for England, but this was on his home ground with the whole of Headingley standing to him,” Nasser Hussain said on Sky Sports.
“It was one of the great innings, one of the great fortnights an England batter has had over the years. He sets the tempo for what Bazball is all about. It’s not about reckless batting, it’s about positive batting.”
Overton, selected primarily as an express fast bowler in place of the injured James Anderson, was within a shot of getting to three figures in his first innings in international cricket when he nicked Boult low to first slip Daryl Mitchell.
The 28-year-old, who resumed on 89, never found the same fluency that had characterised his innings on Friday.
Overton managed one clean drive through the covers for four off Boult on Saturday but repeatedly played and missed.
It was no shock when the New Zealand left-arm quick, who had removed all of England’s top three with a superb display of new-ball bowling, located his outside edge.
The Surrey fast bowler received a rousing reception as he returned to the pavilion and the cheers kept coming.
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.
New batsman Stuart Broad, showing some of the shot-making ability that once enabled him to score a Test century against Pakistan 12 years ago.
Broad embraced England’s new aggressive approach by hitting Boult for 14 runs in three balls courtesy of two fours and a six to the delight of a sun-drenched crowd.
Broad was eventually bowled by Tim Southee for 42 but by then England had gone ahead.
Spectators had already had plenty to cheer as Yorkshire favourite Bairstow, fresh from his match and series-winning 136 against the World Test champions at Trent Bridge, went to 150.
But one ball after Broad’s exit, he holed out off spinner Michael Bracewell to end a brilliant 157-ball innings including 23 fours.