The visiting batting unit struggled to hold its ground against some class bowling from the hosts.
This, with the hosts having piled on an insurmountable total of 519/7 before declaring near the close of play on Day 2.
Only four Caribbean batsmen breached the 20-run mark in response to the Kiwis' huge score as Tim Southee (4/35), Trent Boult (1/30), Kyle Jamieson (2/25) and Neil Wagner (2/33) destroyed the visiting batting unit.
With a nearly unsurpassable lead in the bag and the pitch still offering a lot to the seamers, home team captain Kane Williamson didn't shy away from enforcing the follow-on.
Williamson's decision was immediately vindicated with his threatening pace attack once again building the inroads and leaving West Indies 30/4 at tea after what was a rain-marred second session.
The score soon read 89/6 and a Day 3 finish looked on the cards, but then Jermaine Blackwood (80*) and lower-order batter Alzarri Joseph (59*) went on the counter-attacking and stitched a gutsy 107-run unbeaten stand to perhaps delay what seems inevitable.
The collapse exposed West Indies' longstanding issues with the bat in Test cricket as familiar problems had held them back in England in the last two games after an inspiring victory in Southampton.
Although they couldn't break past Blackwood in the last phase of the day, Southee (1/40), Boult (1/47), Wagner (2/62) and Jamieson (1/33) look on course to put an early end to the proceedings on Sunday (December 6).
West Indies 138/10 & 196/6 in 42 overs (Jermaine Blackwood 80*, Alzarri Joseph 59*; Neil Wagner 2/62) trail by 185 runs versus New Zealand 519/7 declared (Kane Williamson 251, Tom Latham 86; Shannon Gabriel 3/89).