South Africa were 80 for five in their second innings -- 95 runs short of making New Zealand bat again -- at stumps on day four of the series-deciding third Test in Hamilton on Tuesday.
Faf du Plessis was on 15 with Quinton de Kock also on 15.
New Zealand, who need to win to square the series, were all out in their first innings for 489, a lead of 175.
Kane Williamson made 176, Jeet Raval 88 and Colin de Grandhomme 57.
For South Africa, Morne Morkel took four for 100 and Kagiso Rabada four for 122.