The South African bowling attack sent New Zealand to a heavy innings defeat despite a fighting century from Dean Brownlie.
New Zealand started the day on 169 for four, after South Africa bowled them out for 45 on day one and then declaring at 347 for eight on day two.
Set the tough task of setting South Africa a total, New Zealand were bowled out after a late collapse saw them fall from 229 for four on the stroke of lunch to be dismissed for 275 before tea.
The victory gave South Africa a one-nil lead in the two match series with the final fixture starting in Port Elizabeth on 11 January.
Brownlie batted heroically, taking his overnight score of 69 not out to 109 but ended immediately the second new ball was taken when he upper cut a Morne Morkel bouncer to deep backward point with just seven balls remaining in the first session. He hit 13 boundaries and two sixes in his maiden Test century.
But the tourists’ lower order had little answer to the sustained hostility of South Africa’s pace attack and the final five wickets fell in quickly after lunch for the addition of just 23 runs.
Watling’s marathon 42 from 151 balls ended with a classic Vernon Philander delivery which found the edge and provided Graeme Smith at first slip with his 150th catch in just his 106th Test. Doug Bracewell followed shortly afterwards, caught in the gully off the same bowler for a duck.
Dale Steyn bowled Jeetan Patel and James Franklin to claim the ninth wicket of the innings but none of the bowlers was able to claim the wicket of Chris Martin as the New Zealand number 11 was run out without facing a ball.
The second innings wickets were shared between the South African bowlers, including three for 67 by Dayle Steyn, while Vernon Philander earned the man-of-the-match award for his haul of seven for 83.
Day 2: Brownlie resists but SA on top
South Africa maintained their advantage in the first Test at Newlands despite a much improved day by the BLACKCAPS.
The home team declared in a commanding position with a lead of 303 at 347-8 after bowling out New Zealand for 45 on day one. The visitors second dig was more substantial with the visitors getting through to 169 for four at stumps, still 133 runs adrift.
The New Zealand second innings, which started shortly after lunch, looked to be recovering from the first over dismissal of Martin Guptill but they unfortunately lost Kane Williamson on the stroke of tea for 15.
Brendon McCullum and Dean Brownlie then put on a partnership of 89 and saw off the three-prong pace attack but it was spinner Robin Petersen who broke the stand by beating McCullum defences, with the New Zealand skipper out LBW for 51.
Brownlie continued on, reaching his fourth Test half-century from just 44 deliveries but South Africa collected a fourth wicket before the close of play when Jacques Kallis claimed a second wicket when he removed Daniel Flynn (14).
At close, Brownlie scrapped his way to 69 not out and will resume tomorrow with BJ Watling on 10.
Earlier, South Africa started the day on 252 for three, with Alviro Petersen falling early after adding just three to his overnight score of 103 with Trent Boult rocking back his off-stump.
Faf du Plessis was dismissed by Chris Marin 15 and Dean Elgar was nicked out be Boult while AB de Villiers hit 8 fours in 69 before Martin knocked the bails off.
Next over Martin bowled out Robin Peterson to bag three for 63 before Graeme Smith called a halt to the innings.
Boult also impressed with three for 78.
Day 1: South Africa take control on day one
Vernon Philander, Dale Steyn and Morne Morkel tore through the New Zealand batting line up and Alviro Petersen then made an unbeaten century as South Africa took control of the first Test in Newlands.
It was Philander who started the rout with the first five wickets of the day as New Zealand were dismissed for 45, having won the toss and elected to bat. By the close of play South Africa had reached 252 for three, leading their opponents by 207 runs.
Martin Guptill (1) was caught at first slip, Brendon McCullum (7) was bowled, Dean Brownlie (0) nicked off, Kane Williamson was trapped LBW (13) before BJ Watling was caught behind (0) leaving the home side in tatters at 27 for five after 9.1 overs.
Morkel then joined, edging James Franklin (1) to first slip while Dale Steyn continued the onslaught in his second spell, bowling out Doug Bracewell (2) with a near perfect delivery.
Hashim Amla pulled off a stunning catch to remove Jeetan Patel (5) with Morkel picking up his third when Trent Boult (1) edged to the wicket-keeper.
Dale Steyn polished off the innings when he induced a top-edge from Daniel Flynn (8) which he held himself.
Philander ended the innings with five for seven while Morkel took three for 14 and Steyn two for 18 and in the process picked up his 300th Test scalp.
Doug Bracewell New Zealand off to a great start with the wicket of Graeme Smith, trapped LBW, in the second over to send South Africa to lunch at three for one.
However, Hashim Amla made batting look easy on a pitch where many struggled but eventually fell to James Franklin who trapped the number three ranked batsmen in front for 66.
Opener Alviro Petersen continued to steadily accumulate while Jaques Kallis looked in great touch until he caught the edge of a Boult for 60.
Petersen brought up his fifth test century in the penultimate over with a guided shot behind point for two and will resume tomorrow on 103 along with AB de Villiers on 19 not out.