By the break in Dunedin Taylor had advanced his overnight 103 to an unbeaten 144, 10 short of his best set against England in Manchester in 2008.
The hosts resumed on 367 for three with two centurions at the crease but they did not get the positive start they were looking for when Brendon McCullum (113) was bowled between bat and pad by Darren Sammy having added just four to his overnight score.
And when Corey Anderson was caught behind off a leg-side delivery from Tino Best without scoring, it looked like it would be the tourists' morning.
Taylor had other ideas though as he and BJ Watling dug in to take the Black Caps to lunch without further damage.
With boundaries at a premium it was in stark contrast to the previous evening's blitz, but the pair had nevertheless put on 60 for the sixth wicket by the time the interval came around.