New Zealand snared the key scalp of Kraigg Brathwaite in a three-wicket morning session to pick up the scent of victory on day four of the first Test in Wellington on Monday.
Brathwaite's dismissal appeared to snap the West Indies resistance as they went to lunch at 286 for five after resuming the day at 214 for two.
They still require 100 runs with five wickets remaining to make New Zealand bat again after starting their second innings 386 in arrears.
The West Indies had pinned their hopes on Brathwaite anchoring a fightback but his stubborn stand ended when he had reached 91.
He had been assured for 221 deliveries, by far the longest innings by any player in the Test, as he defended calmly and attacked when necessary.
But, after adding 12 to his overnight 79, he was brought down during a brief concentration lapse to an innocuous delivery from spinner Mitchell Santner.
To a ball that held its line, Brathwaite was too late bringing his bat down and was hit on the pads directly in line with the stumps.
It capped a fine morning for the New Zealand spinner who pressured the batsmen throughout an astute seven-over spell which only yielded seven runs.
With the introduction of the new ball, Trent Boult removed Shai Hope for 37 and Matt Henry bowled Roston Chase for 18 as the West Indies slumped to 273 for five.
Sunil Ambris, who made a first-ball duck on debut in the first innings, hooked Boult for six to post the first Test runs of his career.
He had moved to 18 not out at lunch with Shane Dowrich on three.