South Africa's reply began shakily when Boeta Dippenaar tried to leave the fourth ball of the innings, bowled by medium pacer Martin, and dragged it on to his wicket.
Smith and Amla shared a stand of 98 for the second wicket, which was ended when left-arm paceman James Franklin had Smith caught behind by wicketkeeper McCullum.
Smith clipped his aggressive 63 off 64 balls, hitting 10 fours.
New Zealand dismissed Jacques Kallis and Amla in the space of six deliveries. Kallis chopped a delivery from Martin on to his stumps to be bowled for nine while Amla fended a bouncer from medium pacer Styris to Papps at second slip.
Amla hit 10 fours in his 56. Stephen Fleming's 46 was New Zealand's top score and the 55 he shared with Nathan Astle for the fourth wicket was the visitors' best partnership.
Four New Zealanders were dismissed without scoring. Paceman Dale Steyn took three for 43.
South Africa lead the series 1-0 after Ntini took 10 wickets in a 128-run first Test win.
New Zealand lost their first three wickets with just two runs on the board. Ntini had Jamie How caught by AB de Villiers at third slip with the eighth ball of the match.
New Zealand had yet to score their first run four overs later when Michael Papps edged a jagging inswinger from Ntini on to his stumps.
The visitors needed 33 deliveries to move off the mark and they did so when Fleming drove Steyn down the ground for two.
Those were the only runs on the board when Scott Styris edged a delivery from Ntini and was spectacularly caught by De Villiers diving to his left at third slip.
Other deliveries sailed through the slip cordon during the rest of the morning session but none of them went to hand until the last ball before lunch.
A thick edge from Fleming to a delivery from Steyn flew at a comfortable height to second slip where Jacques Kallis dropped what should have been a simple catch.
Kallis made amends eight balls after lunch when he caught an edge Astle offered off Steyn's bowling.
Ntini claimed two wickets in three balls in the fifth over after lunch when he had Fleming caught behind by wicketkeeper Mark Boucher before diving forward to claim an awkward return catch to dismiss Brendon McCullum without scoring.
Six balls later Steyn trapped Vettori in front for two as New Zealand slumped to 82 for seven. Ntini completed his 14th five-wicket haul when he had Chris Martin caught by captain Graeme Smith at first slip for one.