Brook's fast-paced innings of 123 included a century from 91 balls in Wellington on Friday and set the tempo of a day on which 346 runs were scored and 15 wickets fell.
New Zealand were 5-86 in reply to England's 280, having lost Devon Conway, Tom Latham, Rachin Ravindar, Kane Williamson and Daryl Mitchell before stumps.
Brook made the difference in the first Test, which England won by eight wickets, going to the crease at 3-45 and making 171 to deliver a commanding first-innings lead.
On Friday he strode out on to the Basin Reserve with England 3-26 after New Zealand's seamers had dominated the first hour. He left in the last over before tea, run out after having hit five sixes and 74 runs from boundaries.
England were 7-259 when Brook was out, and were finally dismissed for 280 in 53.4 overs.
Brook took three runs from the first nine balls he faced in deference to England's precarious position when he went to the crease. Matt Henry had taken two wickets in his first four overs, all of which were maidens, as the ball seamed sharply on a greenish pitch.
Ben Duckett was caught by Latham at second slip in Henry's second over and Zak Crawley was bowled for 17 when England was 2-21.
Joe Root was out with the total only 26, brilliantly caught by Mitchell at second slip from the bowling of Nathan Smith, then Jacob Bethell (16) fell to Smith with the total 43.
As he did in Christchurch a week ago, and at the Basin Reserve in 2023 when he made 186, Brook seized control of a Test against New Zealand. At the end of his innings on Friday, Brook had scored 437 runs against New Zealand in only six Test innings at an average of 72.8.
He worked his way cautiously, with a single boundary, to 10 runs from 17 balls and then it began: he sent the 19th ball he faced soaring over extra cover, over the embankment fence and out into the street.
There was another six and five fours in his half-century from 37 balls and he found a like-minded partner in Ollie Pope, with whom he rushed to a half-century partnership from 37 balls and century stand from 97 deliveries.
Pope made 66, including a half-century from 65 balls, before he was caught by Ravindra from the bowling of O'Rourke at the end of a partnership that produced 174 runs in just over 36 overs.
Brook reached 123 from 115 balls in 194 minutes, before he was run out from a direct throw in the 53rd over.
Smith finished with 4-86, O'Rourke took 3-49 and Henry ended with 2-43.
England's Brydon Carse had 2-28, after taking a combined 10-106 in the first Test.
