New Zealand reached tea in Dunedin at 575 for eight, with Taylor unbeaten on 206 and Neil Wagner on 14.
Brendon McCullum, who partnered Taylor in a record fourth-wicket stand for New Zealand against the West Indies of 195, added only four runs to his overnight total before he was dismissed for 113.
Taylor, whose previous highest score was an unbeaten 154 against England five years ago, has so far struck 23 fours against the West Indies attack.
McCullum was the first to go. After withstanding a fiery opening barrage from Tino Best he was undone by a delivery from Darren Sammy that cut back between his bat and pad to remove off-stump.
More From This Section
Corey Anderson, who posted a maiden Test century in Bangladesh in October, was unconvincing before he was caught down leg side by Denesh Ramdin without scoring to give Best his second wicket.
BJ Watling helped Taylor rebuild the innings and reached 41 before he became Best's third victim shortly after lunch, nicking a rising delivery to Kirk Edwards at second slip.
Taylor has had one life in his monumental innings so far, when Kieran Powell dropped a sharp chance at short leg off spinner Shane Shillingford.
Best has been the most successful of the West Indies bowlers, with three for 131 while Deonarine and Sammy have two wickets apiece.
Sammy has been having trouble with a leg injury and took himself out of the attack soon after removing McCullum in the morning session.