Dropped chances allow Taylor to hit 129 as hosts take command.
You wonder what sort of card players the West Indies would be; yesterday they badly missed a trick and it haunted them throughout the day at the Basin Reserve.
They won the toss, had the best of the bowling conditions but simply weren't consistently good enough and paid a heavy price.
The key moment of the day, which ended with New Zealand sitting comfortably on 307 for six, came in the 14th over, from the sixth delivery Ross Taylor faced.
He hadn't scored when he pushed hard at a ball from seamer Tino Best and it flew to the left of third slip. It should have been a regulation snare, at catchable height, and was dropped by Kirk Edwards. New Zealand would have been 26 for three. Game very much on.
With every run Taylor made on his way to 129, over 5h 7min and 227 balls, it must have weighed heavily on both the Barbadian and his teammates as they let slip a real chance to take the initiative.
"I thought it was there to hit and it was nice to have a bit of luck," Taylor said last night.
The big thing, though, was that Taylor went on to cash in.
His innings yesterday took his average to 46.52, and enabled him to edge past the only player ahead of him when the day began, of those to have played a minimum of 30 innings, John F. Reid, at 46.28.
After both openers had gone early, Taylor shared stands of 88 with Kane Williamson, 77 with captain Brendon McCullum and 68 with Corey Anderson for successive wickets. None were really substantial, but collectively they shut the door on the West Indies' ambitions.
Four catches were spilled along the way - three from the luckless Shannon Gabriel, who was far tidier than in Dunedin - and three from Taylor's bat.
The worst miss was a complete hash by Best at fine leg, when he finished up doing the splits under a skied hook and the ball flew between his hands.
The seamers, of whom Sammy was perhaps the pick, simply could not hit the right length regularly enough to take advantage of the greenness in the pitch.
"They did bowl a touch fuller but when you're inserted on a greenish wicket, we'll take six for 300 most days of the week," Taylor said.
Now they must scrap hard in the first hour today to avoid New Zealand pressing on to 400, or beyond. New Zealand have a reasonable tail, in Ish Sodhi and Neil Wagner, after the not out pair of BJ Watling and Tim Southee.
Shane Shillingford did take a fine catch at third man to dismissed Taylor, but by then the damage had been done.
Compounding the catching mishaps, the West Indies ground fielding was sloppy. Overthrows never help and wicketkeeper Denesh Ramdin conceded 16 byes, not all to be blamed on the legside waywardness of the bowlers.
They were well behind the over rate for a time, so spinners Shillingford and Deonarine bowled 26 overs in succession after tea, taking two for 73, to catch up.
Runs came in clumps through the afternoon.
Corey Anderson sent Shillingford into the stands twice in quick order; Taylor took four fours from the first 12 deliveries from Best with the second new ball.
But Williamson, fending to second slip, and McCullum, clipping offspinner Narsingh Deonarine to short mid-wicket, were left kicking themselves, having got established and not kicking on.
Taylor reckons there's still interest in the pitch for the seamers.
"We naturally bowl just that little bit fuller and we swing the ball, whereas they nip the ball around a bit."
Translation: he expects New Zealand's fast-medium trio of Southee, Trent Boult and Wagner to bowl smarter than their opponents today.