Tom Latham, the captain, and Rachin Ravindra, the No 4 batter, both scored centuries, guiding New Zealand to a commanding total of 417-4 by stumps, giving them a lead of 481 runs.
Almost half of the Black Caps’ runs today came from boundaries, showcasing their aggressive approach.
The day started with openers Latham and Devon Conway building a solid partnership before Conway was dismissed for 37, with the score at 84.
Kane Williamson joined Latham but fell just before lunch, providing the West Indies with a glimmer of hope.
A missed chance by Roach, dropping Ravindra, proved costly as Latham reached his half century and Ravindra accelerated to 50 in just 52 deliveries.
Latham’s 14th test century and Ravindra’s fourth test ton further solidified New Zealand’s position, with Latham eventually scoring 145 off 250 balls.
Ravindra’s impressive knock of 176 came to an end when he was bowled by Shields, leading to a partnership between Young and Bracewell to see out the day.
Despite their substantial lead, the Kiwis opted not to declare, continuing to bat until stumps with the first ball of day four scheduled for 11am.
