Their first innings looked like being derailed by two needless run-outs in three balls which got rid of Jacob Oram and captain Daniel Vettori.
But with No 9 Kyle Mills belying his position to be a Test-best 46 not out, runs kept coming as he shared an unbroken stand of 72 with Taylor.
Taylor's century was his second in his seven Tests following his 120 against England in Hamilton in March.
He spent 47 minutes in the 90s but Mills kept the scoreboard ticking.
New Zealand, who'd seen Vettori win the toss, resumed on 202 for four with Taylor 67 not out and Oram unbeaten on 22.
All-rounder Oram, whose second innings hundred helped draw the first Test at Lord's, had come in when Daniel Flynn retired hurt after having teeth knocked out by a James Anderson bouncer.
Taylor and Oram had added 113 before three minutes of madness saw their side decline from 249 for four to 250 for six.
Oram, dropped twice on Saturday, first when wicket-keeper Tim Ambrose put down a difficult chance off a steepling Stuart Broad bouncer and when Anderson, running back from mid-on, misjudged a swirling skyer off Monty Panesar, was first to go.
There seemed little danger when Taylor pushed a ball from Broad behind square on the offside.
Bu the tall Oram, on 38, failed to beat Alastair Cook's direct hit from backward point, with third umpire Ian Gould confirming the dismissal.
Two balls later, Vettori was even more careless. Coming back for a second, he crossed the crease but didn't ground either his bat or foot before Ambrose took the bails off following Panesar's throw from square leg.
Again Gould was called upon by Simon Taufel and Vettori was out for one.
With Flynn still unfit to bat, Mills swept left-arm spinner Panesar for six.
Mills then got away with a top-edged four off seamer Ryan Sidebottom, who'd taken two wickets on Friday to go with the six he'd bagged at Lord's.
However, a lofted off-drive against Panesar which went for four and a classical front-foot driven offside boundary off Anderson were testament to the quality of Mills's batting.
Taylor, who'd initially continued where he had left off by square-driving Broad for four, then found runs hard to come by.
But a single off Panesar saw the 24-year-old to a 130-ball hundred with one six and 13 fours.
England took the new ball as soon as they could, after 80 overs, with the Black Caps on 315 for six.
Anderson then had a confident lbw shout against Mills, on 46, rejected by Darrell Hair in what was the Australian umpire's first Test since his involvement in Pakistan's unprecedented forfeit at The Oval in August 2006.