After bowling the Kiwis out for 214, the hosts did not enforce the follow-on as the pitch is getting more and more difficult for the batsmen.
New Zealand's bowlers took six wickets in the last session of the day with only stand-in opener Quinton de Kock (50) offering any resistance as Stephen Cook, Hashim Amla, JP Duminy, captain Faf du Plessis and Stiaan van Zyl went cheaply.
De Kock played a characteristically aggressive innings, hitting the first four balls he faced to the boundary.
Temba Bavuma (25) and Vernon Philander (3) were the unbeaten batsmen at the close of play. Tim Southee and Trent Boult claimed two wickets apiece.
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"The longer the sun bakes down and the cracks widen and the deeper the test goes, the less chance there is for the team batting last. There is no point declaring overnight," South Africa paceman Dale Steyn told reporters.
New Zealand responded in the last session to a pep talk, said all-rounder Doug Bracewell.
"We spoke about giving everything for a session. It's a funny old game, anything can happen yet," he added.
Earlier, New Zealand started their first innings on 38 for three and, despite a determined knock from Kane Williamson, lost wickets regularly until tea when the captain was the last batsman to fall.
Williamson's 77 came off 133 balls and, apart from an entertaining cameo by tailender Neil Wagner, there were few other batting positives for the Kiwis.
Pretoria-born Wagner hit Steyn to all corners of the ground as he crashed 31 in 30 deliveries before the fast bowler had him caught behind.
Steyn ended with figures of three for 66 while Kagiso Rabada picked up three for 62.
The first test was drawn.
(Editing by Tony Jimenez)
