New Zealand were 33 for two at tea, still 269 runs short of avoiding an innings defeat.
Dale Steyn dismissed Martin Guptill for nought in the first over of the second innings.
Captain Brendon McCullum and Kane Williamson resisted for more than an hour before Williamson was caught at second slip shortly before tea.
South Africa declared at 347 for eight soon after lunch. AB de Villiers made 67 before being bowled by Chris Martin, attempting an extravagant stroke to leg shortly before the declaration.
Robin Peterson took the lead beyond 300 with a boundary before he too was bowled by Martin, prompting the declaration.
Trent Boult took three for 78 and Martin three for 63 as the New Zealanders retrieved some pride after a disastrous first day, during which they were bowled out for 45 and then saw South Africa score freely in reaching 252 for three by the close of play.
In mainly overcast conditions, following early morning rain, the New Zealand bowlers made the batsmen work for their runs. South Africa lost five wickets in adding 92 runs in 31.2 overs on Thursday.
Guptill was caught at midwicket, jabbing at a lifting delivery from Steyn in the first over of New Zealand's second innings.
Vernon Philander, who took five for seven in the first innings, again bowled with tight control. As on Wednesday, his first three overs were maidens but whereas his first five overs in the first innings brought five wickets he was unable to claim a wicket.
Philander had an impassioned appeal for leg before wicket against Williamson turned down by umpire Rod Tucker when the batsman was on five. South Africa decided not to seek a review but replays showed the ball would have hit the stumps.
Four runs later the South Africans did ask for a review when they thought Williamson had been caught behind off Philander.
This time, though, the replays were inconclusive, with the ball appearing to flick the batsman's trouser pocket rather than the inside edge of his bat.
Williamson made 15 before he was forced on to the back foot by Kallis and edged a straightforward catch to Alviro Petersen at second slip.