New Zealand pressed for victory with three wickets to reduce England to 193 for five, still 465 runs in arrears, at lunch on the fourth day of the third and final test in Hamilton on Tuesday.
Ollie Pope, who was 17 not out, will head into the second session alongside Gus Atkinson, who was unbeaten on 19.
England, who have already sealed the series by winning the first two tests, resumed their improbable chase for the 658-run victory target on 18-2 in sunny conditions at Seddon Park.
Jacob Bethell continued his impressive start to test cricket with a third half-century of the series but holed out for 76 to give Tim Southee his second wicket in his final innings of test cricket before retirement.
Joe Root had earlier reached his 101st test half century before being dismissed for 54 by spinner Mitchell Santner, whose appeal for lbw was initially turned down but upheld on review.
Brook, whose runs were instrumental to England's wins in Christchurch and Wellington, faced six deliveries for one run before Will O'Rourke had him caught in the slips with the sort of steepling delivery that is fast becoming his trademark.
The England team said that captain Ben Stokes, who is being treated for a left hamstring injury, would bat "if required" in the second innings.