Ollie Pope has led England’s fightback after New Zealand debutant Nathan Smith ripped through the top order at Hagley Oval on Friday morning.
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The tourists were in a spot of bother at 3-45 at lunch on day two after Smith removed England debutant Jacob Bethell and superstar Joe Root in the final over of the morning session.
Bethell edged behind for 10 before Root chopped on for a fourth-ball duck, with Smith boasting figures of 2-12 heading into the break.
However, Brook and wicketkeeper Ollie Pope combined for a 151-run partnership for the fifth wicket to revive England’s innings and put the match back in the balance.
The Yorkshireman brought up his century, his seventh in Tests, in the evening session, needing 123 deliveries to reach the milestone.
England is 5-319 at stumps on day two, still trailing by 29 runs, with Brook (132*) and captain Ben Stokes (37*) unbeaten in the middle.
MATCH CENTRE: New Zealand vs England first Test live scorecard
Kiwis under fire after multiple drops | 00:56
England opener Zak Crawley was removed in the fourth over, opting not to review after New Zealand quick Matt Henry trapped him on the pads.
Fellow opener Ben Duckett was handed a reprieve on 23 after Kiwi captain Tom Latham put down a low chance in the slips cordon. However, the left-hander’s luck ran out in the afternoon session, top-edging a short ball from William O’Rourke towards deep square leg for 46.
Meanwhile, Latham’s woes in the field continued when he dropped another chance in the slips cordon, gifting Brook an extra life on 41 and denying Smith a third wicket.
New Zealand’s frustrations grew when Devon Conway put down an outfield catch early in the evening session, with Brook once again the fortuitous batter. Not long after, Latham was again made to look foolish after a dropping a chance at cover, handing rival captain Stokes a reprieve on 30.
Kiwi debutant knocks over Root for 0 | 00:51
However, all-rounder Glenn Phillips pulled off a stunning catch at gully to break the fifth-wicket stand and send Pope packing for 76, lunging to his right to pluck the one-handed chance while suspended in the air.
Brook continued riding his luck after reaching triple figures, with wicketkeeper Tom Blundell spilling a chance against O’Rourke down the leg side.
Earlier, New Zealand was bowled out for 348 following a career-best performance from England quick Brydon Carse, who claimed 4-64 in the first innings. Phillips notched an unbeaten 58, his fifth Test fifty, while batting with the tail.