The first two fell in seven balls.
Sunil Ambris edged Colin de Grandhomme to first slip with the opening ball of the session.
Wicketkeeper Shane Dowrich played an indescribably bad shot to give a gentle catch to backward point off Neil Wagner's first ball of the next over.
Kemar Roach went lbw to de Grandhomme. He sought a DRS referral immediately, which suggested he had hit the ball.
Replays, however, showed his bat was nowhere near the ball and it would have struck near the top of the stumps.
Captain Jason Holder skied a catch to mid wicket to give Wagner his best match figures.
After Miguel Cummins suffered a painful blow just above his knee from Trent Boult, he was bowled by the same bowler.
Wagner finished with two for 102 which gave him a match haul of nine for 141, his best test analysis in his 33rd test.
The match is New Zealand's 14th victory against the West Indies, against 13 defeats and 19 draws.
New Zealand bossed the game from the start, after sending the West Indies in on Friday and dismissing them for 134.
Centuries to Colin de Grandhomme, the second fastest by a New Zealander in tests, and debutant wicketkeeper Tom Blundell pushed New Zealand to 520 for nine.
The second test starts at Hamilton's Seddon Park on Saturday.
