The tourists fought back in the final session at Newlands yesterday and ended day two on 169 for four, 133 runs behind South Africa, who followed up New Zealand's embarrassing opening effort of 45 all out - their third-lowest Test score - with 347 for eight declared.
Dean Brownlie's unbeaten 69 was a rare bright moment for the visitors as he put on 89 with his captain Brendon McCullum for the third wicket.
The Black Caps made a good start from the first ball of the second over yesterday as Trent Boult got one to nip back at Alviro Petersen (106), who could only get an inside edge before the ball clattered into the stumps.
AB de Villiers, who began the day unbeaten on 19, was tentative, scoring his first boundary in the seventh over as the hosts attempted to build on what was already a significant first-innings lead.
The Proteas suffered a blow in the 73rd over when Chris Martin pitched one up which swung away from Faf du Plessis, with the batsman edging to Kane Williamson in the slips for 15.
At 280 for four De Villiers and Dean Elgar, playing in just his second Test, built slowly until consecutive fours from the one-day captain off Boult yielded 10 runs in the 82nd over.
New Zealand struck again in the 89th over as Elgar edged a rising Boult delivery to the wicketkeeper BJ Watling who took a simple catch for 21. De Villiers fell in just the second over after lunch for 67 when he was bowled by Martin.
The 38-year-old struck again in his next over when he bowled Robin Peterson
This led to the home captain Graeme Smith declaring, leaving New Zealand to bat out the remaining 56 overs of the day 302 runs behind.
A tough task was made even harder when Martin Guptill was dismissed in the last ball of the first over, pushing a tame Dale Steyn leg-stump half-volley to Hashim Amla at midwicket.
McCullum and Williamson dug in, with just six runs coming in the first six overs.
After battling through 46 balls for 15, Williamson became the second New Zealander to needlessly lose his wicket playing away from his body to edge a wide Jacques Kallis delivery to Petersen at second slip.
Brownlie was the exception to the rule for the visitors as he raced on to 24 from just 19 balls with four boundaries, although he was dropped twice in consecutive overs.
At the other end the untroubled McCullum brought up his 25th Test fifty off 96 balls in the last ball of the 29th over as the Kiwis moved to 117 for two.
However, his resilience was to last just one more over as he was trapped lbw by Peterson for 51.
Brownlie reached his fourth Test half century off 44 balls and he and Daniel Flynn put on 37 for the fourth wicket before Flynn became Kallis's second victim, edging to De Villiers to leave New Zealand 155 for four.
Follow us @SprtNationalUAE