Following a similar pattern to last week's initial test, where England secured victory by eight wickets, Brook and Ollie Pope came to the rescue of the innings after the top order collapsed at 43-4. The duo formed a strong fifth-wicket partnership, adding 174 runs to resurrect the team's chances.
Will O'Rourke broke the partnership by dismissing Pope off a leading edge for 66 an hour before the second break and had England skipper Ben Stokes caught in the slips for two.
New Zealand finally got the key wicket of Brook in farcical circumstances when he was run out by all-rounder Nathan Smith for 123 to bring up tea. Chris Woakes will resume on 15 not out.
Brook had brought up his third century in four tests in New Zealand from 91 balls with a single through point, having smashed nine fours and five sixes to rescue England for the second match in a row.
The 25-year-old scored an entertaining 171 last week in Christchurch and he and Pope put on 151 runs for the fifth wicket as England recovered from 71-4 to post a score of 499.
Earlier, New Zealand skipper Tom Latham won the toss and chose to send out his four-pronged seam attack out on a greenish wicket at Basin Reserve.
Zak Crawley made a statement of intent with a four and a six off Tim Southee in the first over but the problems began for England when Matt Henry came on with the wind behind him at the other end.
The tall paceman's first four overs were maidens and included the wickets of Ben Duckett, caught in the slips by Latham for a duck, and Crawley, bowled through the gate for 17.
With Southee not having as much luck, Smith was brought on and had Joe Root caught brilliantly in the slips by Daryl Mitchell for three before Jacob Bethell gloved a bouncer behind for 16.
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