Deonarine and Shivnarine Chanderpaul then combined for a 129 run stand for the fifth wicket, taking the score from a precarious 104-4 to a solid 263-6.
Chanderpaul was incredibly patient, hitting 51 off 137 deliveries but it was Vettori who struck again to have the seemingly immoveable left-hander caught at mid-off.
Deonarine was far more aggressive striking 106 off 124 before holing out and in doing so handed Neil Wagner his first wicket of the day.
Wagner, who ran in hard from ball one, was rewarded with the late wicket of Devon Thomas who was caught-behind after cracking a quick 32.
Vettori was the pick of the attack, finishing the day with four for 48 while Wagner has two for 50.
Earlier, the New Zealand tail managed to add another 12 runs to the overnight score of 137-8 with Nethula and Martin both making four and Wagner left unbeaten on six.
Captain Permaul picked up two wickets his morning to finish with 3-34 while Kemar Roach, who picked up all his wickets on day one, returned figures of 4-34.