The hosts, chasing a record 455 to win, were bowled out for 255 on the final day, only defiant fifties from Alastair Cook and Jos Buttler holding up the New Zealanders who sealed their fifth test victory in England.
The hosts had resumed on 44 for no wicket and Adam Lyth failed to add to his overnight 24, feathering a swinging ball from paceman Trent Boult through to wicketkeeper Luke Ronchi.
Gary Ballance unconvincingly negotiated 25 deliveries for six runs before Boult produced a venomous full delivery that crashed into the left-hander's stumps.
Ian Bell, on one, turned a bouncing ball from spinner Mark Craig straight into the hands of Kane Williamson at leg-slip and Joe Root was brilliantly caught off Craig for a second-ball duck by Tom Latham at short leg.
With England's slim hopes of victory all but over, Cook and Ben Stokes adopted a cautious approach, although the all-rounder produced a couple of trademark crisp boundaries to entertain a sparse crowd on a chilly day at Headingley.
The pair added 40 for the fifth wicket but Stokes was out for 29 just before lunch, caught by Ronchi as he attempted an ambitious cut off Williamson.
Cook's innings, lasting nearly four hours, ended on 56 when he was trapped lbw by part-time spinner Williamson before Moeen Ali was bowled for two, shouldering arms to a ball from Matt Henry that struck his off stump.
Stuart Broad made a breezy 23 before he was bowled by Williamson but Buttler and Mark Wood shared a gritty ninth-wicket partnership of 42.
Tim Southee, with the second new ball, had Wood caught in the slips by Craig for 17 and Buttler's brave three-hour knock ended on 73 when he offered no stroke to Craig and was out lbw.
England won the first test at Lord's by 124 runs.
(Editing by Tony Jimenez and Ken Ferris)
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