Kavem Hodge scored his second Test century on Saturday as the West Indies reached 381-6 at the end of the third day of the third Test at Mount Maunganui, 194 runs behind New Zealand and avoiding the follow-on.
The 32-year-old crawled to his century off 224 balls, hitting 12 boundaries and being dropped on 74 by Daryl Mitchell who shelled a difficult chance at slip off Ajaz Patel.
He faced 33 balls to get through the 90s including a long stoppage on 97 after he was hit a painful blow in the box by a Michael Rae delivery.
Hodge shared in an 81-run partnership with Justin Greaves which edged the visitors closer to the follow-on target of 375, and fifty stands with Tevin Imlach and Alick Athanaze.
Hodge was unbeaten on 109 at stumps with Anderson Phillip the other not out batsman on 12.
New Zealand received a spark from an unlikely source when Mitchell trapped Greaves lbw for 43, just his fourth Test wicket in his 35th match.
Batting suddenly looked a lot harder, as Roston Chase came and went, trapped lbw by Patel.
The West Indies said their leading batsman, Shai Hope, would not have batted on Saturday because of food poisoning, but Kemar Roach, who suffered a hamstring injury on day one, would bat if required.
Phillip came to the crease and should have been out for two when edging Patel to wicketkeeper Tom Blundell, but New Zealand did not appeal. He was then dropped on eight from Patel's bowling by Rae at mid-on.
Jacob Duffy had 2-79 from 31 overs, while Patel took 2-94 in 33 overs to end his unwanted record of being the bowler to take the most Test wickets without a single one at home.
Patel's 86th Test wicket was his first in New Zealand, bowling Athanaze in the middle session some 2,562 days since his first Test in New Zealand and with his 394th ball on home soil.
England's Billy Bates, who took 50 wickets between 1882 and 1887, all in Australia, has regained the dubious honour in the Test history books.
New Zealand made a breakthrough straight after lunch as Imlach fell for 27, caught behind by Blundell from the bowling of Rae.
Hodge and Athanaze combined for a 61-run partnership with the latter playing a series of nice drives and flicks as he looked to find form.
Having confidently moved to 45 a moment of indecision saw Athanaze gift Patel his wicket.
He attempted to leave a ball well down the legside, only for it to deflect off his inner thigh and on to the stumps.
Jacob Duffy with the breakthrough early on day three!
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The West Indies resumed on Saturday at 110-0 and added only one run before Duffy struck in the second over as John Campbell edged to Tom Latham at second slip without adding to his overnight 45.
It ended the first West Indies century opening stand since February 2023.
Duffy doubled up when he bowled Brandon King, who had begun the day on 55, for 63.
New Zealand declared their first innings on Friday at a mammoth 575-8, anchored by Devon Conway's epic 227 and captain Latham's 137.
NEW ZEALAND Tom Latham (capt), Devon Conway, Kane Williamson, Rachin Ravindra, Daryl Mitchell, Tom Blundell (wkt), Glenn Phillips, Zak Foulkes, Michael Rae, Ajaz Patel, Jacob Duffy.
WEST INDIES John Campbell, Brandon King, Kavem Hodge, Shai Hope, Alick Athanaze, Roston Chase (capt), Justin Greaves, Tevin Imlach (wkt), Kemar Roach, Anderson Phillip, Jayden Seales.