After the home side added another 150 runs through the first half of the day to be eventually dismissed for 460, so taking a first innings lead of 239, the Black Caps negotiated 41 overs to the close for the loss of Brendon McCullum. (Agencies)
Opening batsman Tom Latham extended the pattern of resolute defiance that has brought him three consecutive half-centuries in the series to be unbeaten on 30.
Kane Williamson (38 not out) has been similarly obdurate and the pair will be seeking their third century partnership of the tour and much more going into the fourth day.
West Indies' only glimmer of hope in separating the pair came just before the close when Latham edged a delivery from part-time spinner Chris Gayle that dropped just short of Sulieman Benn at slip.
New Zealand, who lead the series 1-0 after winning the first match of the three-Test series in Jamaica last week, were forced to adjust their opening combination due to a stomach ailment that kept Mark Rutherford off the field for the first half of the day.
McCullum took on the responsibility but the captain did not last long, trapped leg-before for three by Jerome Taylor.
There were no further casualties, but on a pitch that is expected to be more variable in bounce over the final two days, the tourists will be hard-pressed to produce a rearguard similar to the one that earned them a draw against India in Wellington four months ago.
Jermaine Blackwood's adventurous innings of 63 was the highlight of the latter half of the West Indies first innings as they resumed in the already healthy position of 310 for five.
Coming to the crease after the swift fall of nightwatchman Kemar Roach to Trent Boult, the debutant's first scoring shots were an edged four through the slips and a commanding six over long-on.
He added five more fours and another six as the West Indies pushed hard to extend their first innings advantage.
For the second time in the series, the experienced Shivnarine Chanderpaul was adjudged lbw to Ish Sodhi offering no shot, falling for 47.
But captain Denesh Ramdin added 76 entertaining runs for the eighth wicket with Blackwood before the innings came to a swift end in mid-afternoon, Sodhi taking two of the last three wickets to fall to finish with figures of four for 96.
Although the leg-spinner claimed the most wickets in the innings, he proved expensive together with the other support bowlers, off-spinner Mark Craig and medium-pacer Jimmy Neesham.
Frontline seamers Boult and Tim Southee bore their responsibilities manfully and frugally, but the ease with which the West Indies batsmen scored off the others almost resulted in their efforts being in vain.
After the home side added another 150 runs through the first half of the day to be eventually dismissed for 460, so taking a first innings lead of 239, the Black Caps negotiated 41 overs to the close for the loss of Brendon McCullum.