Stuart Broad sparked a sensational New Zealand collapse after Daryl Mitchell made a hundred to leave England needing 277 to win the first Test at Lord's on Saturday.
World Test champions New Zealand, who had been 251 for four, lost their last six wickets for 34 runs on the third morning -- three falling to successive Broad deliveries -- as they were dismissed for 285.
There have been only three successful fourth-innings run chases of more than 200 runs in Lord's Test history, with England's best at the 'Home of Cricket' the 282 for three they made against New Zealand in 2004.
And Alex Lees, who had hit four boundaries in his 20, was then bowled leaving a Kyle Jamieson delivery that came back into the left-hander, with England 31 for one at lunch.
After rain delayed Saturday's scheduled start by 30 minutes, New Zealand resumed on 236 for four in their second innings, a lead of 227.
Mitchell was 97 not out overnight and Tom Blundell unbeaten on 90 after they had come together Friday with the Black Caps in trouble at 56 for four.
The 31-year-old son of former All Blacks rugby coach John Mitchell wasted no time in reaching his second century in 10 career Tests, off-driving Broad for three from his first ball of Saturday's play.
After waiting 366 deliveries to take the fifth wicket, England astonishingly collected three in three balls for a team hat-trick.
Broad, recalled along with James Anderson after England's two all-time leading Test wicket-takers were controversially left out of a series loss in the Caribbean, was the man to make things happen.
He dismissed Mitchell and Jamieson, either side of Ollie Pope running out Colin de Grandhomme.
Mitchell was caught behind for 108 off a Broad delivery that nipped away to end a New Zealand record fifth-wicket partnership against England of 195.
Broad's next ball led to a huge lbw appeal against de Grandhomme, who carelessly left his crease and was run out by Pope's direct hit from the slip cordon before the seamer bowled Jamieson for a golden duck.
Blundell, who had been watching the wickets go down from the other end, took his score to 96.
But he fell short of a place on the honours board when Anderson had him plumb lbw before Matthew Potts, who took four wickets for 13 runs in New Zealand's first innings 132, continued his fine debut by removing Ajaz Patel.
Concussion substitute and England debutant Matt Parkinson, summoned after Jack Leach was injured fielding Thursday, ended the innings with his first Test wicket when the leg-spinner had Tim Southee caught at slip.