Ross Taylor scored his first Test double-hundred as New Zealand put the West Indies in deep trouble on the second day in Dunedin.
Taylor, having been 103 overnight, was unbeaten on 217 as the Black Caps declared shortly after tea on 609 for nine, surpassing his previous best of 154 not out.
By stumps the tourists were in further trouble on 67 for two - 542 behind - having earlier slipped to 24 for two.
Brendon McCullum could only add four runs to his overnight 109 before being bowled by Darren Sammy and Corey Anderson was caught behind off Tino Best without scoring.
But Taylor and BJ Watling dug in to take the Black Caps to lunch without further damage.
After the resumption Best surrendered 13 runs in one over, which saw Taylor reach 150, but the bowler gained his revenge in his next over when Watling edged a lifting delivery to second slip for 41 to end the partnership at 84.
Taylor then upped the ante as he plundered four boundaries and 18 runs off one over from Shannon Gabriel, who found his fortunes had improved little from day one as he continued to feed the batsmen a consistent diet of long-hops.
And the moment of the day came as Taylor drove Narsingh Deonarine for four, then clipped him for three next ball to bring up his maiden double-ton just before tea.
A couple of sixes from Neil Wagner took New Zealand past 600 for the fourth time in Tests, but when he was run out for 37 that was the signal for a declaration.
West Indies lost Kirk Edwards for no score in the third over, edging Trent Boult to slip, and Keiran Powell caught behind off Southee soon after.
But Darren Bravo played nicely to finish the day unbeaten on 37 alongside Marlon Samuels, with the pair facing a daunting task when play resumes.