The tourists reached lunch at 71-1 after 29 overs, with Kraigg Brathwaite not out 41 and Kirk Edwards unbeaten on three.
The West Indies went into the match without the suspended Shane Shillingford, who was replaced by spinner Sunil Narine, and are without first Test double-centurion Darren Bravo, who was injured during net practice on Wednesday.
Bravo was replaced by Brathwaite, who, in his first Test of the series, was dropped on 13 when he drove Neil Wagner through the hands of Tim Southee at short cover point.
The few nicks they generated fell short of the slips cordon and it took medium left-armer Wagner to make the breakthrough in the second hour of play.
He dropped one short to Kieran Powell that found the edge of the bat to be caught behind by BJ Watling for 26.
Wagner had figures of one for 10 off seven overs.
New Zealand lead the three-match series 1-0 after winning the second Test in Wellington last week by an innings and 73 runs.
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