The former skipper, who scored an unbeaten double century in the series opener, was dismissed shortly before close of play at Wellington's Basin Reserve for 129 when Shane Shillingford pulled off a diving catch.
In-form Taylor arrived at the crease with the home side in deep trouble at 24-2 on a green wicket and was dropped before he got off the mark.
In conditions that favoured the bowlers, the 29-year-old forged half-century partnerships with Kane Williamson, Brendon McCullum and Corey Anderson to swing the match New Zealand's way, taking the sting out of the second new ball with BJ Watling.
Taylor has amassed a total of 362 runs in just three innings and been dismissed just once. He also passed 4,000 Test runs during his innings and now has an average of 46.52, topping the list of New Zealand batsmen who have played a minimum of 20 innings.
After his early life when dropped in the slips by Kirk Edwards, Taylor offered another opportunity on 122 when Tino Best spilled a catch at fine leg. That came just after Taylor had belted 13 runs off one over by the West Indies quick.
But he was seldom under pressure as he faced 227 balls and hit 15 boundaries before slashing at Shannon Gabriel and being well caught by Shillingford.
New Zealand's cause was also helped by the inability of West Indies strike bowlers Best and Gabriel to maintain the good line and length that saw them claim openers Peter Fulton and Hamish Rutherford in quick succession.
Fulton, whose leg before wicket first ball dismissal was overturned on appeal, did not make the most of his reprieve as he poked at a Darren Sammy delivery outside off-stump a few overs later and was caught behind for six.
Rutherford, dropped by Sammy on eight, made only three more runs before chasing a shorter Best delivery, which he edged to wicketkeeper Denesh Ramdin.
Kane Williamson, returning to the New Zealand line-up after missing the Dunedin Test with a thumb injury, scored freely until he reached 45, when he flashed at a wide Best delivery to be caught by Sammy in the slips.
McCullum and Anderson, like Williamson, also made solid starts before being undone.
McCullum spooned an innocuous Narsingh Deonarine delivery to Edwards without adding to his teatime score of 37 while Anderson fell to Shillingford for 38 after earlier hitting the spinner for two sixes.
Best was the most successful of the West Indies bowlers, with two for 66 off 14 overs while part-time spinner Deonarine proved the most economical with 1-39 off 16 overs.