New Zealand cleaned up the final three South Africa wickets on Thursday morning to dismiss the tourists for 238 before reaching 40 for one at lunch on day two of the first Test in Dunedin.
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Resuming on 191 for seven, Jacques Rudolph added the four runs he needed to post his 10th Test half-century but then departed for 52. He was caught at point by Trent Boult off the bowling of Doug Bracewell.
Vernon Philander earlier became the first wicket of the day and Chris Martin's fourth scalp of the innings when he was caught at gully by Kane Williamson for 22.
Imran Tahir's departure wrapped things up for the Black Caps, the number 11 batsman run out by a combination of Bracewell and Daniel Vettori as he attempted a third run.
New Zealand's reply got off to a rocky start when opener Rob Nicol (six) edged a Philander delivery to Graeme Smith at first slip.
However, Martin Guptill (16 not out) and Brendon McCullum (18 not out) helped the hosts regroup and see out the rest of the session with no further dismissals.
Martin claimed three quick wickets after tea on Wednesday in a blistering evening session as the Proteas slumped from 86 for one.