The home team came into final day with the score on 103-4, with still a long way to go to reach their 373-run target, but had kingpin Joe Root still at the crease.
England batting unravelled quite quickly on the fifth morning as Emilio Gay was the first to walk back to the pavilion, edging behind off seamer Nathan Smith for 10.
Then in the same over it was disaster for the hosts when Root was run-out after Henry Nicholls had a superb direct-hit that left the champions batter short after Jamie Smith had called for a quick single.
The Black Caps could sense victory was close but Smith and Gus Atkinson then stood firm for a stubborn 75-run partnership.
The stand was broken when Atkinson fell lbw to left-arm spinner Micthell Santner for 19 while Jofra Archer did not long before he was dismissed for 2.
Smith went to his half-century but Josh Tongue was also run-out with another direct hit from Santner before the victory was sealed when Smith was out for 60.
New Zealand became the first time ever to win a Test series in England after going 1-0 down following the defeat at Lord's in the first Test.
The series will be remembered for the chaotic retirement of England captain Ben Stokes but the tourists will not care one bit as they move up to third in the World Test Championship table.
Pakistan debutant Razaullah, batting at number 9, smashed a record-equalling nine sixes to keep his team in the third Test against England at Edgbaston, with home needing a target of 130 to win.
New Zealand white-ball captain Mitchell Santner has declined a lucrative offer from Australian Big Bash League side Adeliade Strikers to remain in contention for Test selection.
England were on 154-4 at stumps on the first day of the third Test against Pakistan at Edgbaston after the visitors once again folded with bat to be 133 all out.
Kevin Pietersen is set to return to the England setup after being appointed as a specialist mentor to the men's white-ball teams ahead of the 2027 World Cup.
