Martin Guptill struggled against hostile bowling until the eighth over before edging Vernon Philander to AB de Villiers at second slip with just six runs to his name.
Rob Nicol, who had also looked uneasy facing anything short and outside the off stump, was not out on 10, with Brendon McCullum also on 10.
South Africa declared their second innings midway through the middle session at 435-5 with Jacques Rudolph unbeaten on 105 -- the third centurion of the innings after Graeme Smith (115) and Jacques Kallis (113).
New Zealand had their hopes up early in the day with Kallis adding only six runs to his overnight 107 before he played an uncharacteristic lofted shot off left-armer Trent Boult and was caught by Nicol at midwicket for 113.
But de Villiers joined Rudolph at the crease and they built on South Africa's lead, adding 70 runs for the fifth wicket.
The partnership was broken when New Zealand turned to part-time spinner Kane Williamson, who had de Villiers caught at deep midwicket by McCullum for 29, leaving Mark Boucher (34 not out) to partner Rudolph until the declaration.
South Africa declared after Rudolph brought up his century, the sixth of his career, with a four off Daniel Vettori.
Doug Bracewell was the most successful of the New Zealand bowlers with three for 70 while Williamson finished with 1-16 and Boult 1-93.