Dean Brownlie's maiden Test century helped New Zealand to 232 for five at lunch on the third day after South Africa had declared their first innings closed at 347 for eight on Thursday.
However five wickets fell for 23 runs in a lower order collapse in the second session and the New Zealanders ended up 27 runs short of making the world number one side bat again.
Brownlie, who had been brought into the team as a replacement for Ross Taylor who opted out of the tour after he was replaced as captain by Brendon McCullum, resumed on day three with wicketkeeper BJ Watling, who was on 10.
The duo were resolute in the morning session and a frustrated Proteas' outfit were forced to watch as Brownlie reached his century with a big six over long-off from the bowling of Robin Peterson.
South Africa eventually got their man in the penultimate over before lunch as Brownlie cut a Morne Morkel delivery straight to Alviro Petersen on the point boundary having made 109.
Watling and James Franklin continued to frustrate the Proteas in the first hour following the break as they looked to avoid an innings defeat.
Three dropped catches had marred the hosts fielding display on day two and Franklin was next to be given a reprieve as ro Petersen grassed his second chance of the innings at gully.
A double-strike by Vernon Philander shortly before the drinks break crippled the New Zealand innings though, as Watling edged to first slip and was out for 42.
Doug Bracewell was caught at gully for a duck to reduce the Black Caps to 252 for seven and Jeetan Patel (8) was clearly rattled by the fearsome pace of Dale Steyn before eventually chopping on to his stumps.
The final two wickets fell in quick succession, as Franklin too played on to his stumps for 22 having lasted 103 minutes to leave New Zealand on the brink at 274 for nine.
The Test match ended in a fittingly shambolic fashion for the Black Caps when Chris Martin was run out one delivery later without having faced a ball after being sent back by Trent Boult.
Philander won the man-of-the-match award for his match figures of 7-83, which included five for seven in the first innings. He has now captured 74 wickets in 13 Tests at 17.40 runs each since making his debut in November 2011.
"I think it's a special attack, it's a special place. This unit, and the way we operate, having each guy know his role," he told a news conference.
"There's days where he (Steyn) attacks and I do a holding job, and then vice versa. I think as a unit, we understand each other well and that's the way we operate.
"I think with the intensity of our bowling lineup we're going to exploit the weaknesses somewhere along the line. I think Brownlie played exceptionally well, but giving his wicket away there just opened up the whole tail to our bowlers."
McCullum also praised the qusality of the South African pace bowling.
"The Australian attack of a few years ago was pretty relentless as well and it's no surprise that they were the number one in the world at that stage as well with the ability to take 20 wickets," he said.
"This South African team posseses that too and they keep coming hard at you and constantly put you under pressure. Their seam attack is right up there in terms of the best attacks and is certainly the number one attack in the world at the moment.
"It's pretty disappointing to lose a Test match inside three days. It hurts immensely and there were a very disappointed bunch of lads in the change room after day one and that hasn't changed."
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