The Black Caps moved to a dominant first innings lead of 313 runs reaching 447 for 9 by stumps on day two in Wellington.
The highlight of the day was a brutal 105 off 74 balls from New Zealand allrounder Colin de Grandhomme who took the game away from the West Indies.
Ross Taylor (93) fell just short of a 17th Test century and shared a 127 run stand with Henry Nicholls after losing overnight partner Jeet Raval (42) early on.
De Grandhomme entered the fray after a flurry of wickets left New Zealand 281 for 6 and allowed the Black Caps to take complete control of the match.