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Not only were they rolled for their third worst total, 45, after winning the toss, but by stumps at Newlands, the hosts were 207 ahead, having reached 252 for three by stumps.
Opener Alviro Petersen was on 103 and AB de Villiers 19.
Only Kane Williamson managed even double figures as New Zealand capitulated meekly in 19.2 overs, or 100 minutes. It was the lowest test score since India's 42 at Lord's in 1974.
New Zealand captain, Brendon McCullum, made a bad misjudgment of his team's batting talents at the toss.
He wanted to get on the front foot in the game and it went horribly wrong.
The South African bowling was formidably good, but it was helped by lame batting.
Fast-medium Vernon Philander maintained both his fine record against New Zealand, and his terrific overall record, taking five for seven in his opening six-over spell.
Morne Morkel's three for 14 and Dale Steyn's two for 18 rounded things off nicely as they ensured South Africa's opening batsmen would head out to the middle before lunch.
The consistently accurate Philander has now taken 72 wickets at just 16 runs apiece halfway through his 13th test.
Against New Zealand, he's taken 26 wickets at a stunning 12.7 each.
When Steyn removed one of Doug Bracewell's stumps, he had 300 test wickets, the fourth South African bowler to that milestone, after Shaun Pollock (421 wickets), Makhaya Ntini (390) and Allan Donald (330).
In the afternoon it was champion allrounder Jacques Kallis' time to click over another significant number.
When he sliced Bracewell wide of gully to reach 23, he had surpassed 13,000 test runs, joining Indians Sachin Tendulkar and Rahul Dravid, and recently-retired Australian Ricky Ponting in that elite group.
New Zealand's only bowling successes were removing Graeme Smith in the second over, then Hashim Amla and Kallis, both in the 60s, after consecutive stands of 107 and 104 with the steady Petersen, who completed his fifth test century, off 170 balls with 11 fours and a six, near the end of a sunlit day.
New Zealand's batting misery was compounded by a poor fielding performance and a bowling effort which was unable to make much mileage as whatever demons lurked in the pitch earlier in the day went to sleep.
Five batsmen were caught either by wicketkeeper de Villiers or Graeme Smith at first slip as they failed to cover the ball on or outside their off stump.
The innings lasted only 100 minutes and contained just five fours. At times it was kids against men, and New Zealand were completely outclassed on the day, which amply demonstrated the gulf between world No 1 and No 8.
South African captain Smith had made it clear the day before the match that his team had determined to start the test, their first in a month and first at home in almost a year, in strong, assertive fashion.
His team responded just as he'd requested, leaving a devastated New Zealand to try and regain some face in the remainder of the match.
South African officials' worst fears about the disparity between the teams, and likely financial loss out of potentially at least one day not required, were realised