After centuries from Devon Conway, Rachin Ravindra, and Henry Nicholls powered the visitors to a massive 476-run first-innings lead, the bowlers wasted no time finishing the job on day three.
Debutant Zakary Foulkes starred with figures of 5/37 in the second innings — the best-ever debut bowling performance for a New Zealander in Test cricket.
The result marked New Zealand’s largest-ever win by an innings, and the third-biggest in Test history.
The all-time list is topped by England’s innings-and-579-run demolition of Australia in 1938, followed by Australia’s innings-and-360-run victory over South Africa in 2002.
Matt Henry, who claimed a five-wicket haul in the first innings, was a standout throughout the series, taking 16 wickets at an astonishing average of 9.12. His efforts earned him the Player of the Series award, while Conway was named Player of the Match for his 153-run knock.
Under stand-in captain Mitchell Santner, the Black Caps had already secured a nine-wicket win in the opening Test.
The clean sweep followed an undefeated run in a preceding T20I triangular series involving South Africa, where New Zealand edged the Proteas by three runs in the final.