A well-crafted century by captain Chris Gayle helped the West Indies to 278 for seven at stumps on day four in Napier.
It was the first time Gayle had reached triple figures in a Test match since his knock of 317 against South Africa in April 2005.
And it could not have come at a better time for his side who were left reeling at 106 for four early in the day after Jeetan Patel struck twice in two balls to have Xavier Marshall and dangerman Shivnarine Chanderpaul dismissed.
Gayle's unbeaten 146 included six sixes, one of which landed on the roof of the stand at McLean Park, and 13 fours but in between these flashes of power-hitting he showed great patience and overcame a bout of cramp late in the day as he led his side to a lead of 214 runs with three wickets in hand.
His 124-run stand with Brendan Nash, who scored his second successive half-century, came at a crucial time for his team following the dismissals of Marshall and Chanderpaul in the 16th over of the day.
Marshall edged his delivery behind and the ball was deflected by wicket-keeper Brendon McCullum to Ross Taylor who took a comfortable catch.
But it was Chanderpaul's departure, when he hit a full toss straight back to Patel, which sparked scenes of jubilation in the New Zealand camp.
Nash survived the hat-trick ball and from then on he and Gayle, who had resumed on 36 as the West Indies started the day 62 for two, frustrated the New Zealand bowlers as they showed incredible patience against the spin bowling of Daniel Vettori and Patel, who had figures of three for 59 at the lunch break.
The pair batted through the second session with Gayle bringing up his eighth Test hundred with a nervy single after a rare mis-field by Patel saw a run-out chance go begging.
Nash then followed up his 74 from the first innings with another half-century, his seventh boundary taking him to 53 in 137 balls.
