Tim Southee leads the Black Caps from the field after his final test. Photo: Photosport
England, who had already sealed the series by winning the first two tests, crumbled to 234 all out after lunch in their improbable chase for 658 runs to sweep the series.
Captain Ben Stokes, who is being treated for a left hamstring injury sustained on Monday, did not bat in England's second innings to further hasten the conclusion.
The end came swiftly with England, who looked determined to go down fighting before the break, losing their last three wickets in 12 deliveries for the addition of three runs.
Mitchell Santner (4-85) was named Player of the Match after ripping through the England tail to give New Zealand their biggest ever win by runs and inflict the fourth-worst defeat by runs on the tourists.
"It's obviously pleasing to finish in that fashion," said New Zealand captain Tom Latham.
"We certainly knew we weren't quite at our best those first couple of games, but I think the way we came in here and were able to adapt to the surface was very pleasing."
Southee failed to add to his extraordinary tally of sixes on Monday and will retire with 98 but he did take two wickets in his final test innings to finish his career with 391, the second highest for a New Zealander behind only Sir Richard Hadlee.
"We're certainly leaving one of the greats behind, but I'm sure he's got a bright future ahead of him, whatever that may be," Latham added.
Although the tourists were disappointed to finish with such a crushing defeat, even on Tuesday there were some positives to go along with becoming the first England team to win a series in New Zealand since 2008.
England captain Ben Stokes with the series winning Crowe-Thorpe trophy. Photo: Photosport
Jacob Bethell had earlier continued his impressive start to test cricket with a third half-century of the series before he holed out for 76 to become Southee's final test victim.
Joe Root reached his 65th test half-century before being dismissed for 54 by Santner but Harry Brook was unable to find the runs that were so instrumental to England's wins in Christchurch and Wellington.
The Player of the Series faced six deliveries for one run before Will O'Rourke, a standout for New Zealand, had him caught in the slips with the sort of steepling delivery that is fast becoming his trademark. Gus Atkinson blasted 43 off 41 with seven fours and one six in a defiant rearguard but once he departed with a miscued slog to Glenn Phillips at deep cover, the end was not long in coming.
"We want to come out and win every game that we play," said Stokes.
"It's obviously disappointing as a team to finish like we have done but ... the first two test matches is where it really counted for us, and that's where we played our best cricket."
- Reuters