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 having previously been dropped on nought, 122 and 127.
New Zealand wicketkeeper BJ Watling was on eight at the close with Tim Southee on nine.
The 29-year-old Taylor had held the hosts innings together after the West Indies' bowlers reduced New Zealand to 24 for two in the first session after winning the toss and choosing to bowl.
The hosts' middle order, however, were guilty of throwing away their wickets after they had made promising starts. Kane Williamson was dismissed for 45, captain Brendon McCullum for 37 and all-rounder Corey Anderson for 38.
Despite not kicking on to bigger scores they all shared in productive partnerships with Taylor of 88, 77 and 68 runs, to tip the balance of the match slightly in the hosts favour.
"We would have taken that at the start of the day. It probably didn't do as much as we thought it would at the start of the day but 300 for six is good," Taylor told Radio Sport.
Taylor's dismissal in the 88th over of the day was the first time he had been dismissed in the series. He has scored 362 runs in his three innings.
"I got congratulated by Shiv Chanderpaul and I said 'oh I was a bit lucky' and he said 'you need luck in this game and you never take a test hundred for granted'," he added of the three chances he gave the West Indian fielders.
"I had a bit of luck to get off the mark other than that I was pretty composed and played each ball on its merits until I got to about 110 and then fatigue set in."
West Indies captain Darren Sammy had won the toss for the second successive game and had little hesitation in asking the hosts to bat on a green Basin Reserve 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 Kirk Edwards at second slip with New Zealand's score on 26.
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 McCullum went back and punched Narsingh Deonarine directly to Kirk 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 the West Indies immediately asked for a review with the 'hot spot' technology showing the ball hitting his bat.
The third and final match of the series is at SeddonPark in Hamilton from December 17.
Image: New Zealand's captain Ross Taylor
Photograph: Vivek Prakash/Reuters
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