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Starting the day at 157 for four, trailing by 247, overnight pair Dean Brownlie and BJ Watling got through the first half hour unscathed but once Brownlie was removed, the end came quickly.
The final wicket fell 35 minutes before lunch.
The last five wickets tumbled for just eight runs in the space of 30 balls as pace kings Dale Steyn and Morne Morkel wiped out the tail, New Zealand finishing on 211.
The teams now turn their attention to the three-match ODI series, starting in Paarl on Saturday night (NZT).
It was New Zealand's 23rd test loss to South Africa in 40 matches and completed a grim fortnight for the tourists.
They were comprehensively outplayed by the world's best team, but even allowing for that, New Zealand need to take a hard look at themselves, as they were below acceptable standards too often in the series.
Watling completed his second half century of the test with a crisp four behind point off burly seamer Rory Kleinveldt, and Brownlie followed Watling to that mark shortly after, having grafted 166 minutes and 129 balls, with eight fours.
The pair resumed last night, having come together half an hour after tea on the third day, and were relatively untroubled through the opening half hour from Kleinveldt and spinner Robbie Petersen.
The new ball, due after 13 overs last night, posed the big question. If Watling and Brownlie could safely negotiate the initial burst from speedster Dale Steyn and Morne Morkel it would be a significant achievement.
However, champion allrounder Jacques Kallis had other ideas and enticed Brownlie to chase a ball outside his off stump and edge a catch to the wicketkeeper just before the new ball was due.
The partnership had produced 98 runs from 219 balls.
Watling's form in this match, in which he has been the most technically proficient New Zealand batsman, against raised the question of where he should bat when England arrive next month.
He began his test career as a specialist opener against Pakistan in 2009, making an unbeaten 60 on debut in Napier.
However, the problem with putting him back up the order is his other task of wicketkeeping. Opening and taking the gloves is a stretch these days.
Colin Munro, after a duck in his first test innings, didn't look comfortable against Petersen's spin but Morkel's fifth delivery with the new ball had him caught at third slip for 15 and the tail abjectly failed to wag.
Man of the match Steyn took three for 48 to finish with eight for 65 in the match.
He ended Watling's resistance with a cracking delivery which clipped the outside of his off stump. Watling's second 63 of the match came off 117 balls with 11 fours.
Doug Bracewell, Trent Boult and Neil Wagner were whisked away in no time.
- David Leggat