The Black Caps dismissed the tourists for 223 in the 35th over, after having them 56/6 early, but Brook singlehandedly saved his side from absolute disaster, hitting 132 off 101 balls, including 11 sixes.
NZ bowler Matt Henry took the scalp of England opener Jamie Smith with the first ball of the innings and wickets fell regularly, until Brook and Jamie Overton put on 87 runs for the seventh wicket.
Brook and tailender Luke Wood compiled 57 runs for the last wicket, before Brooks was caught by Nathan Smith, from the bowling of NZ skipper Mitch Santner.
Zak Foulkes emerged as the best bowler with figures of 4/41, including Ben Duckett and Joe Root in the second over of the day.
Black Caps squad: Mitchell Santner (capt), Michael Bracewell, Mark Chapman, Devon Conway, Jacob Duffy, Zak Foulkes, Matt Henry, Kyle Jamieson, Tom Latham, Daryl Mitchell, Rachin Ravindra, Nathan Smith, Kane Williamson, Will Young.
