At tea, New Zealand were 267 for four to lead the West Indies by 133 runs with six wickets remaining.
Henry Nicholls was 66 not out, his fifth half-century, with Mitchell Santner on 12.
The West Indies had singled out Taylor as the wicket to get if they were to have any chance of salvaging something from the Test after their meagre first innings of 134.
But by the time they dismissed New Zealand's senior batsman -- with judicious use of the review system after an lbw appeal had been rejected -- they were already more than 100 runs behind.
Taylor was on 93 and closing in on his 17th century to equal the New Zealand record held by his mentor, the late Martin Crowe, and current captain Kane Williamson, when he was trapped in front by Kemar Roach.
There were two noises which suggested an inside edge and when the initial appeal was turned down the West Indies went for a second opinion, where the video review showed only the pad had been hit.
It ended a 160-ball innings by the 33-year-old who had given few chances until the new ball was taken two overs before his dismissal.
For most of the day Windies skipper Jason Holder had placed defensive fields with a limited cordon behind the stumps, and Taylor moved into the 90s when he edged a ball from Roach through the huge gap between second slip and gully.
New Zealand resumed the day at 85 for two and added 182 runs for the loss of two wickets in the first two sessions of play after Jeet Raval went for 42 in the 10th over of the morning.
The West Indies had their hopes briefly raised with the third ball after lunch when Nicholls was caught behind off a poorly executed pull shot, only for video replays to show Jason Holder had over-stepped for a no ball that kept Nicholls in the game.
It was an error the West Indies could ill-afford as they unsuccessfully employed the short-ball barrage that had worked so well for New Zealand on day one.
They seldom troubled Taylor while Nicholls, although at times indecisive with the pull shot, picked up runs with ease during their 127-run stand for the fourth wicket.
Roach was the most successful of the West Indies bowlers with three for 63.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)