New Zealand have grabbed late wickets in the Dunedin gloom but South Africa are 191 runs in front in the first Test.
The Proteas finished Saturday on 6-224, after grinding their way through the first two sessions then losing their way with three wickets going in the final period.
Faf du Plessis was not out 56 and Vernon Philander on one. They have a 191-run lead but rain is forecast for Sunday's final day.
Dean Elgar, after scoring 140 in the first innings, again top-scored with 89.
He faced 548 balls in his two innings, the most by a South African in a Test in New Zealand.
Elgar moved to his 50 when he blasted a lofted drive through the hands of Colin de Grandhomme at short cover.
He was closing in on what would have been his seventh Test century, when he skied a catch to Kane Williamson at wide mid-off.
Temba Bavuma (6) was bowled by Mitchell Santner when a defended ball spun back onto his stumps and then Jeetan Patel dismissed Quinton de Kock (4) again this summer, bowling him when he beat the outside edge of the bat.
Neil Wagner finished the day with figures of 2-57, Trent Boult 1-34, Patel 2-72 and Santner 1-37.
The hosts have more injury problems after batsman Ross Taylor had torn his calf, with Boult leaving the field on Saturday suffering soreness in his hip/groin area.
New Zealand were only able to get one wicket each of the first two sessions, Hashim Amla (24) in the morning and JP Duminy (39) after lunch, before Elgar, Bavuma and de Kock went in the fading light late in the day.
In the morning, drizzle delayed the start but the Black Caps were guilty of dropped catches and poor DRS reviews.
Duminy was on six when Tom Latham dropped a simple catch at first slip.
Elgar also had a let-off when BJ Watling could only get the tip of a glove to an outside edge.
They wasted their two DRS chances, seeking reviews which replays clearly showed were not out.
Duminy was involved both times - the first caught behind review showed the ball hit his pad, while the second lbw review revealed a thick inside edge.
They could have had Duminy on 20 when they opted not to review a declined lbw decision where the television replay showed it might have been given out.
South Africa scored 308 in their first innings and New Zealand responded with 341.
