A maiden Test century from South Africa's David Bedingham would help set a target of 267 for New Zealand to chase in the final innings in Hamilton.
Proteas stars Dane Piedt and Dane Paterson combined for eight wickets as New Zealand fell 31 runs short of South Africa's first-innings total on day two of the second Test in Hamilton.
The second Test between New Zealand and South Africa at Seddon Park saw Rachin Ravindra help limit the visitors to 220 for six at stumps on day one.
New Zealand tightened their grip on the first Test against a weakened Proteas side at Mount Maunganui on Tuesday, after Kane Williamson smashed his second Test century of the match.
Mount Maunganui pales in comparison to the mountain the Proteas batters have to climb after being dominated on day two of the first Test against New Zealand.
The Proteas will field a completely new-look Test side against New Zealand on Sunday, but stand-in captain Neil Brand says the players are ready to embrace the challenge.