Recalled paceman Kemar Roach led the way with a wicket from the third delivery of the day and his younger teammates Justin Greaves, Jayden Seales, Ojay Shields and Johann Layne all pitched in to maintain the pressure.
Kane Williamson, granted a life on 33 when debutant Shields bowled him through the gate off a no-ball, scored his 38th Test half-century in a 93-run partnership with Tom Latham, but three wickets in four overs put the Black Caps on the rack at 4-103.
The Windies, who last won a Test in New Zealand in 1995, drove home the advantage after tea, with Shields finally getting his maiden Test wicket with a sizzling in-swinging yorker to remove Tom Blundell for 29.
However, allrounders Michael Bracewell and Nathan Smith stopped the rot with a stand of 52 for the seventh wicket to take the home side past the 200 mark.
Smith departed for 23, caught at short midwicket off the spin of West Indies skipper Roston Chase, and Bracewell holed out for 47 off a Shields bouncer to exit with his second Test half century in sight.
Zak Foulkes and Jacob Duffy, both four not out, will resume on day two to defend the final New Zealand wicket.
West Indies had won the toss and chose to field with Chase's decision vindicated when Roach had Devon Conway caught in the slips for a duck in the first over, giving the 37-year-old quick a 285th Test wicket.
Wet weather disrupted the early part of the day with a first rain interruption in the fourth over and another in the 11th over forcing an early lunch break before the skies cleared.
Justin Greaves broke the second-wicket partnership by removing Williamson for 52 when the batting great shoulder armed a delivery and the ball flew off his bat to Alick Athanaze in the slips.
He got Latham two overs later for 24, the New Zealand captain attempting a drive but only managing a thick edge behind.
Seales soon bowled Rachin Ravindra with a full straight yorker that took out the off stump and Will Young continued his poor run of form with a 38-ball 14 before he nicked the ball to the slips.
