A five-wicket haul by Jacob Duffy gave New Zealand a 64-run first-innings lead over the West Indies with the tourists all out for 167 in the first Test on Wednesday.
At stumps on day two in Christchurch, New Zealand were 32-0 in their second innings to be 96 ahead.
Devon Conway was not-out 15 with Tom Latham on 14.
In 16 deliveries following a rain break in the final session Duffy removed the final four West Indies wickets for only two runs.
The fast bowler had earlier dismissed the West Indies top scorer Shai Hope for 56 to finish with career-best figures of 5-34.
Half-centuries from Hope and Tagenarine Chanderpaul provided the backbone of the West Indies innings in a 90-run stand for the third wicket.
Hope, wearing sunglasses under heavily overcast skies because of an eye infection, went to the crease with the West Indies in early trouble at 10-2.
Despite being affected by conjunctivitis and needing breaks to be treated with eyedrops, he produced a near-chanceless sixth Test half-century.
But on 56 he allowed a short ball from Duffy to brush his gloves on its way to wicketkeeper Latham and was gone.
Matt Henry struck twice with a double-wicket maiden having Roston Chase and Justin Greaves caught behind by Latham as the West Indies slumped from 100-2 to 106-5.
Chanderpaul battled his way to 52 from 169 deliveries before he was undone by Zak Foulkes as the floodlights came on under murky skies after the tea break.
The West Indies opener had been dropped twice, on five and 24, by Conway at leg slip.
But Conway, leaping to his left, pouched the third chance sent his way at mid-wicket.
After a 30-minute rain interruption Duffy removed Tevin Imlach (14), Johann Layne (nought), Jayden Seales (two) and Ojay Shields (nought).
The West Indies took just three balls to end the New Zealand first innings at the start of the day, without adding to their overnight 231.
Foulkes, the last man out, was then immediately in the action with the ball, removing John Campbell for one with his first delivery.
Will Young completed the dismissal with a smart one-handed catch to his left at third slip, but then dropped a regulation chance when Alick Athanaze, on four, edged Henry.
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However, the scoreboard had not moved before Henry bowled Athanaze in his following over with a ball that nipped back sharply.