The tourists made a shaky start to their reply, reduced to 24-2 before recovering to reach 67 without further loss by the close but they face a monumental task to avoid defeat.
Taylor, who a year ago was in the doldrums when dumped as New Zealand captain, proved that disappointment was well behind him as became only the 13th New Zealander to reach 200 in a Test innings.
Along the way he shared in a 195-run partnership with replacement skipper Brendon McCullum — a record fourth-wicket stand for New Zealand against the West Indies.
Taylor was at the crease for more than eight hours, faced 319 balls and hit 23 boundaries without risking a lofted shot.
Four of those boundaries came in one over from Shannon Gabriel as the workload told on the West Indies quicks after a leg muscle strain forced Darren Sammy out of the attack.
Throughout his marathon innings, Taylor offered only one sharp chance when he was dropped on 131 by c at short leg off spinner Shane Shillingford.
After New Zealand resumed the day at 367-3, the West Indies made early inroads with the removal of McCullum for 113 and Corey Anderson without scoring.
BJ Watling (41) restored order with Taylor in an 84-run stand for the sixth wicket before the West Indies engineered a second mini breakthrough.
Tino Best claimed the scalp of Watling and Narsingh Deonarine removed Tim Southee for two to have New Zealand at 472-7 before Ish Sodhi (35) and Neil Wagner (37) helped Taylor to get New Zealand past the 600-run milestone.
New Zealand declared at their fourth-highest Test score following the dismissal of Wagner after the tailender and Taylor had belted 34 runs in five overs after the tea break.
The aggressive Best, with his short-pitched deliveries, was the most successful of the West Indies bowlers, returning figures of three for 148 while Sammy and Deonarine finished with two wickets apiece.
The West Indies faced 24 overs before stumps and were quickly in trouble when Trent Boult angled a ball across Kirk Edwards, who edged it straight to Peter Fulton for a regulation slip catch.
Edwards was out for a duck and fellow opener Kieran Powell followed in similar fashion soon after when caught by wicketkeeper Watling for seven.
Darren Bravo, not out 37, and Marlon Samuels on 14, both survived confident appeals as they held the innings together until the close of play.
Boult, who constantly troubled the batsmen, ended the day with 1-7 after bowling five maidens among his eight overs. Southee, the other wicket taker, had 1-15 off seven overs.