Captain Brendon McCullum and Dean Brownlie are at the crease for the Black Caps, who lost Martin Guptill for a duck and Kane Williamson for 15.
At 33 for two at tea and following their dismal first-innings showing of 45 all out - their third-lowest Test score - McCullum's side are facing a heavy defeat after the hosts posted 347 for eight declared.
The Black Caps made the ideal start in the first ball of the second over of the day as Trent Boult got one to nip back and bowl Alviro Petersen before Chris Martin pitched one up which swung away from Faf du Plessis, with the batsman edging to Williamson in the slips for 15.
New Zealand struck again in the 89th over as Dean Elgar, playing back, edged a rising Boult delivery to wicketkeeper BJ Watling who took a simple catch for 21.
AB De Villiers fell in just the second over after lunch for 67 when he was bowled by Martin and the 38-year-old struck again in his next over with Robin Peterson the next South African to be bowled as his off stump was disturbed attempting to play a leg-side shot.
Graeme Smith then declared and a tough task was made even harder when opener Guptill was dismissed with the last ball of the first over, pushing a tame Dale Steyn leg-stump half-volley to Hashim Amla at mid-wicket.
McCullum and Williamson dug in, with just six runs coming in the first six overs before a Steyn half-volley was dispatched to the mid-off boundary by Williamson.
The Black Caps continued to build slowly and survived a review in the ninth over when South Africa felt that Williamson edged a Vernon Philander delivery to De Villiers, although nothing showed up on hotspot and the not-out decision stood.
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.