Opener Devon Conway's epic innings ended on 227 Friday as the West Indies showed some fight after lunch on day two of the third test, but New Zealand piled on the runs to go past 500 at Mount Maunganui.
Jayden Seales trapped Conway lbw shortly after lunch to make it 432-4 and the West Indies removed two more batsmen as New Zealand went to tea at 508-6.
New Zealand had resumed after lunch at 424-3 at lunch, looking to punish an under-strength West Indian attack missing Kemar Roach, who strained a hamstring late on day one.
Shai Hope was also absent, falling ill overnight and remaining at the team hotel.
The tourists did not help themselves in the field. Kavem Hodge dropped Conway when he was on 206, and Daryl Mitchell was dropped by Justin Greaves at second slip when he was on nine.
Seales was first to strike in the afternoon, darting one past the inside edge of Conway and into the pads, a ball that would have clattered into middle and leg stumps.
Conway's three runs after lunch saw him go past the top score of his batting idol, Neil McKenzie, who made 226 for South Africa against Bangladesh in 2008.
Mitchell fell for 11, getting a thick edge down the legside from Roston Chase which was expertly taken by wicketkeeper Tevin Imlach.
Tom Blundell gave Seales his second wicket, when an attempted cut was edged to Imlach.
Seales had 2-100 from 33 overs at tea and Justin Greaves had 2-76 from 28 overs.
Rachin Ravindra batted through the session, moving to 38 at tea, combining for a 47-run partnership with Glenn Phillips on 28.
Earlier, Conway powered to a second test double century after he resumed the day on 178, with New Zealand 334-1.
He was quickly back in the groove as he drove his first ball of the day to the cover boundary for four.
He then knuckled down as the West Indian bowlers found good movement off a bouncy surface.
Jacob Duffy, who came in as a nightwatchman on Thursday evening in fading light, fell for 17, edging Jayden Seales to wicketkeeper Tevin Imlach.
Conway then brought up his second test double-century – his first since making 200 on debut in 2021 against England at Lord's – cutting a Seales short ball to the point boundary.
His 200 came off 316 balls, with 28 fours, but he was dropped soon after reaching the milestone.
Greaves, who struck to remove Williamson just before lunch for 31, caught by Imlach.