The skipper, who promised ahead of the Test that his team would play attacking cricket against Indian spinners, led from the front with an aggressive 127-ball 113, smashing two sixes and 16 fours in his seventh Test hundred.
Wicket-keeper Kruger van Wyk hit an 85-ball 63 not out for his maiden Test half-century, while opener Martin Guptill cracked a 79-ball 53. Doug Bracewell was unbeaten on 30 when play was called off due to bad light and rain.
Bracewell and van Wyk have so far put on 82 for the unfinished seventh-wicket stand.
Left-arm spinner Pragyan Ojha, who opened the attack in overcast conditions, was the most successful bowler with 4-90.
Taylor completed his hundred in style, cutting Ojha for a four and then lofting the spinner over long-off in the same over for his second six. His century came off just 99 balls.
He was out lbw while attempting to sweep Ojha soon after the tea-break.
Off-spinner Ravichandran Ashwin and Ojha, who shared 18 wickets in India's victory by an innings and 115 runs in the opening Test in Hyderabad, had to work hard for success on a good batting track.
New Zealand, who collapsed to 159 in their first innings and 164 in the second at Hyderabad, put in an improved batting performance, thanks to Taylor's brilliant knock.
New Zealand were under pressure at 89-3 following Ojha's double-strike in the morning, but Taylor propped up the innings with a 107-run stand for the fourth wicket with Daniel Flynn (33).
Taylor counter-attacked to neutralise the Indian spinners, slog-sweeping Ashwin over square-leg for the first six of the match and then smashing four boundaries in an over from Ojha.
The New Zealand captain, who reached his half-century off just 46 balls, also drove paceman Zaheer Khan through the covers and then straight for two successive fours.
New Zealand lost two wickets in the afternoon as Flynn fell lbw while attempting to sweep Ashwin and James Franklin (eight) was superbly caught by Suresh Raina at mid-wicket off Ojha.
Ojha earlier removed Kane Williamson (17) and Guptill to put pressure on New Zealand, but Taylor dominated the Indian attack with an exciting strokeplay in the afternoon.
New Zealand lost opener Brendon McCullum for no score in the second over after electing to bat, before Guptill and Williamson steadied the innings with a 63-run stand for the second wicket.
But Ojha dismissed both the batsmen, trapping Williamson leg-before and then having Guptill caught by Gautam Gambhir at mid-wicket.
Guptill, dropped on 17 by Virat Kohli at third slip off Zaheer, hit eight fours in his 12th Test half-century in 26 matches.
The New Zealand opener played some attractive shots, hitting seamer Umesh Yadav for three fours in an over and then reaching his half-century with a boundary in the bowler's next over.
India retained their side, while New Zealand brought in paceman Tim Southee in place of Chris Martin.