The right hander held the innings together, despite losing Hamish Rutherford (19) and Ross Taylor (six), with 58 not out as New Zealand reached 123 for three when bad light stopped play for the day. Brendon McCullum was also unbeaten on 23 at the close.
Earlier, West Indies were bowled out for 317, taking a slim 24-run lead on first innings following a good late knock from fast bowler Jason Holder.
The hosts resumed on Saturday on 169 for two with Kirk Edwards (42) and Darren Bravo (eight) and the pair moved the score on to 197 before left arm paceman Neil Wagner ended their stand.
West Indies continued to build small partnerships but when Kemar Roach was dismissed for a duck by Trent Boult they were 277 for seven and staring at a first-innings deficit.
Holder (38) then provided stubborn resistance with Shane Shillingford (10 not out).
Jimmy Neesham finally had Holder caught by wicketkeeper BJ Watling from a rising delivery that brushed his gloves and the innings quickly folded.
Wagner finished with figures of four for 64.
The three-match series is locked at 1-1 after New Zealand won the first test in Jamaica and the hosts took the second in Trinidad.
(Reporting by Greg Stutchbury, editing by Tony Jimenez)
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