Kyle Jamieson took five wickets as the West Indies slumped to 124-8 at stumps on Saturday, trailing New Zealand by 336 runs in Hamilton.
The Black Caps kicked on with bat in hand, with Henry Nicholls building on his brilliant Friday century by continuing his dominance over the West Indies bowlers.
Nicholls surpassed the 150-run mark to take his team past 400 as New Zealand built towards a big first-innings total.
Nicholls eventually departed for 174 before Neil Wagner smashed 66 from 42 deliveries down the order as New Zealand reached 460.
The West Indies again struggled to get going with their batting and was in trouble early on at 29-4 as Jamieson and Tim Southee began to pick up wickets.
Jermain Blackwood made 69 but failed to get any sort of assistance from his fellow batsmen with Jamieson taking 5-35, while Southee bagged three of his own.