England, who had already sealed the series by winning the first two Tests, crumbled after lunch on Tuesday 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.
Mitchell Santner took 4-85 after ripping through the 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 Black Caps 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."
🇳🇿 391 wickets— ICC (@ICC) � 98 sixes with bat in hand� #WTC21 winnerTim Southee's prolific Test career comes to a close � pic.twitter.com/FxgCuAoKSVDecember 17, 2024
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 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, there were some positives to go along with becoming the first England team to win a series in New Zealand since 2008.
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 (one) was unable to find the runs that were so instrumental to England's wins in Christchurch and Wellington.
A beautiful piece of bowling from Will O'Rourke to dismiss Harry Brook for the second time in the Test. Follow play LIVE in NZ with TVNZ DUKE, TVNZ+, Sport Nation and The ACC. LIVE scoring | — BLACKCAPS (@BLACKCAPS) https://t.co/gATDuNgLhk 📲 #NZvENG #CricketNation pic.twitter.com/JKb1ATx32JDecember 16, 2024
The Player of the Series faced six deliveries before Will O'Rourke had him caught in the slips. Gus Atkinson blasted 43 off 41 but once he departed 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."
