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.
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.