The Black Caps, holding a first-innings lead of 349, declared their second innings on 179 for four just before play commenced, setting the Proteas a daunting victory target of 529.
Though South Africa never appeared close to reaching it, they displayed some resistance before seamer Kyle Jamieson (4-58) made crucial breakthroughs, while spinner Mitchell Santner (3-59) cleaned up the tail to bowl them out for 247.
“Pretty happy, I think any time you win a test match inside four days it’s always pretty pleasing,” said New Zealand skipper Tim Southee.
“We know that any South African team is going to fight, they are very passionate people, and we knew that they were going to be up for it over this test match.”
Despite New Zealand having never beaten South Africa in a Test series in nearly a century of attempts if they seal the deal in the second Test in Hamilton next week, the breakthrough victory will be significant.
The Proteas arrived in New Zealand with a severely weakened squad featuring eight uncapped players, as Cricket South Africa prioritised their financially profitable Twenty20 competition (SA20).
However, New Zealand could only play against the opposition in front of them and convincingly outshone them over four mostly sunny days at Mount Maunganui.
Local hero Kane Williamson became just the fifth New Zealander to achieve a century in each innings, while all-rounder Rachin Ravindra was awarded Man of the Match for his mammoth 240 in the first innings.
“Rachin we’ve seen over the last six months or so is a special talent and he showed in this test match what he’s capable of. I’m sure he’s got a bright future,” added Southee.
Despite New Zealand’s seamers not producing many fireworks in their own conditions, they took wickets in clusters, breaking up key partnerships and restricting South African batsmen to only one half-century across the match.
South Africa skipper Neil Brand was left rueing dropped catches on day one that granted reprieves to Williamson and Ravindra.
“It’s very deflating,” said the 27-year-old, who took eight wickets in his first Test.
“I felt day one, we were in the game there and if you take those two chances, you never know what will happen. But yeah, completely outplayed by a very good New Zealand team.”