Brook was 136 not out from 131 balls, with Joe Root on 72 at the Basin Reserve, the Yorkshire pair having pushed their unbroken stand to 216 runs after coming together at 21 for three in the morning.
New Zealand captain Tim Southee won the toss and elected to field on a grassy wicket, the gambit paying immediate dividends with three wickets falling in the first hour.
But from there, it was all downhill for the hosts as Brook and Root took over on a sunny afternoon and steered England to 3-101 by lunch.
The batters were untroubled for the best of the part of an hour after the break until Henry sent a ball thudding into Root's pads when he was on 31.
The former England captain narrowly survived an lbw review, with the technology showing the ball hitting leg stump - yet not enough to over-rule the umpire's not out decision.
That was as close as New Zealand got to a breakthrough, with the aggressive Brook appearing impregnable and Root playing a steady support role to the 24-year-old sensation.
Brook attacked any delivery with a hint of looseness, smashing part-time seamer Daryl Mitchell for two sixes over his head in successive balls to race towards his century.
Root reached his 57th fifty in tests by pushing a single off Bracewell, one ball before Brook cut the part-time spinner to the fence for four to bring up his hundred.
The duo hiked the run-rate after those milestones, with New Zealand quick Neil Wagner bleeding nearly seven runs an over after being badly roughed up in the series-opening defeat at Mount Maunganui.
Though Southee wasted two of New Zealand's three reviews in the first half-hour, it had otherwise been a promising start for the home side.
Matt Henry had opener Zak Crawley feather an edge to be caught behind for two, before Ollie Pope was out for 10 after edging Henry to Bracewell at third slip.
Southee had a driving Ben Duckett out for nine, with Bracewell diving to his left to pull down a spectacular, one-handed catch in the slips.
Unchanged England won the pink-ball opener by 267 runs and are bidding to win their first Test series in New Zealand since 2008.
