Taylor, who scored a career-best 217 not out in the drawn first Test at University Oval in Dunedin, was caught at deep backward point for 129 shortly before the close of the first day's play of the second Test.
His dismissal with 14 balls remaining in the day's play meant New Zealand wicketkeeper BJ Watling (eight) and pace bowler Tim Southee (nine) will resume on Thursday.
Taylor had come to the wicket with New Zealand in deep trouble at 24 for two after being asked to bat on the green Basin Reserve pitch by West Indies captain Darren Sammy.
The 29-year-old, who was dropped on nought, adopted the same approach that took him to his first Test double century last week and patiently worked the ball around to share in important partnerships throughout the day.
"I think I'm in the best mindset that I've ever been in," Taylor told reporters.
"It's probably a little cliched saying 'play in the now' but it's working for me at the moment," he added. "I just try to keep the same tempo the whole time.
"At the start of the day I felt a little bit like Dunedin. But after 20-30 balls, I got to where I wanted to be.
"It was nice to fight that and I suppose that comes with a little bit of experience."
New Zealand could have easily collapsed early when Taylor was dropped by Kirk Edwards at second slip without scoring and with the hosts on 26 for two, but the middle order combined to put on 233 runs to guide their side to a slim advantage.
Despite their important partnerships, they would be kicking themselves for getting out when bigger scores were on offer.
Kane Williamson was dismissed for 45, captain Brendon McCullum for 37 and all-rounder Corey Anderson for 38, though Taylor said the pitch still had plenty of life in it if the bowlers hit the right spots.
"Most balls did something. I wouldn't say it was nipping round corners but the odd ball kept you honest," Taylor who was also dropped on 122 and 127 in his innings, added.
"Any time you get 30 or 40 you'd like to kick (on) but ... the odd ball does something and keeps you honest. That's what happened today.
"I think there's still a little bit in there. A big first hour tomorrow will set up what hopefully is a good day.
"If we can get to somewhere around 380-400, (it) will put West Indies under some pressure."
West Indies' bowlers had got some early assistance from the green wicket, capturing openers Peter Fulton for six while Hamish Rutherford was dismissed for 11.
The double-strike left the hosts floundering at 24 for two and they could have been in further danger when Taylor was dropped by Edwards at second slip.
Taylor and Williamson, however, settled the innings before the recalled Williamson, who had recovered from a broken thumb, was dismissed after lunch.
McCullum and Taylor took the home side through to 186 for three at tea before the captain punched Narsingh Deonarine directly to Edwards at short mid-wicket after the break.
Anderson was also looking comfortable before he tried to sweep Shane Shillingford and got a bottom edge onto his bat with the ball ballooning to Kieran Powell at silly point.
The 22-year-old was initially given not out but West Indies immediately asked for a review and the technology showed the ball hitting his bat.