Harry Brook's calculated century propelled England back into the first Test against New Zealand on the second day in Christchurch.

Brook was dropped four times in his unbeaten 132, without which England might already be on the way to defeat.

The Kiwis dropped six overall, three by captain Tom Latham, in England's 319-5, 29 runs behind.

Some outstanding New Zealand bowling reduced the tourists to 71-4, including 21-year-old Jacob Bethell out for 10 on his Test debut.

Brook combined with Ollie Pope for a fifth-wicket partnership of 151. Pope, standing in as wicketkeeper, was pushed down to number six from his usual number three and made 77, the first time he has passed 29 in seven Test innings.

It took a truly breath-taking moment to remove Pope, Glenn Phillips holding a spectacular flying catch at gully from a full-blooded cut at Tim Southee.

England captain Ben Stokes, playing in the city of his birth, looked closer to his best for 37 not out in an unbroken stand of 97 with Brook, though Stokes was another put down by Latham on 30.

All this after New Zealand were bowled out for 348, pace bowler Brydon Carse taking the two wickets to fall in the morning to end with 4-64.

These two sides often produce compelling contests. The 2019 World Cup final and New Zealand's one-run win in Wellington 18 months ago are two recent classics, and this has the potential to be another thriller.

New Zealand should be well on top. They were wasteful with the bat on day one, then shambolic with their catching on Friday.

The fielding did a disservice to their seamers, who gave England a lesson in using the new ball. Whereas England struggled to find the right length on the first morning, New Zealand were relentless.

Bethell could not have been given a much tougher assignment as England's new number three, yet did not look out of place.

Brook and Pope hung in long enough for the ball to get older and the sun to come out. Conditions eased, England hauled themselves back into the match.

Given the small deficit and depth of their batting, England are marginally on top, though a strong burst with the second new ball on Saturday morning could tip the balance towards New Zealand once more.

For all the lingering questions about England's Bazballing approach to batting, the Brook-Pope stand was a counter-punch when it was needed most. They rattled along at nearly five an over.

There was fortune, even without the missed chances. Pope needed to time to settle, both men slashed through and over the slips. Brook's let-offs came on 18, 41, 70 and 106.

If Phillips, at gully off the bowling of debutant Nathan Smith, held Brook's first offering, England would have been 77-5. The next two drops, Latham at slip off Smith and Devon Conway at deep mid-wicket off Phillips, were borderline farcical.

Brook passed 2,000 Test runs in his 36th innings. Only the great Herbert Sutcliffe got there faster for England. Paradoxically, Pope's runs at number six will only increase the questions over whether he should be England's number three.

Given his fluctuating year and the lives gifted to Brook, Pope must have been cursing his luck that he was the victim of Phillips' gravity-defying brilliance. Even Brook gave him a consoling pat on the way off.

Brook, who had already pulled two sixes, scooped Southee for four then cut the same bowler to go to his seventh Test ton. Then came the final miss, a flick down the leg side off Will O'Rourke was parried by keeper Tom Blundell. Leg-byes were given, but a review would have confirmed bat.

From 319-8 overnight, New Zealand immediately had Southee bounced out to begin Phillips' eventful day. He was hit on the head by Carse, dropped by Joe Root, reverse-scooped Chris Woakes for four, pulled off a superman dive to avoid being run-out and was left unbeaten on 58 when O'Rourke was yorked.

The cool, cloudy conditions were ideal for seam bowling and New Zealand's quartet were superb.

Matt Henry's nip-backer continued Zak Crawley's awful record against New Zealand – he averages only 10 against the Kiwis – and brought Bethell to the crease.

The left-hander took 13 balls to get off the mark and struck two sweet boundaries off Smith before edging to give Smith a first Test wicket. When Root played a limp shot to chop on in the same over, England were in the mire.

Ben Duckett, dropped on 23 by Latham, took on the short ball after lunch, only to hook the pacey O'Rourke to long leg and fall for 46.

England were flawed, allowed back into the game by New Zealand's drops – one of the six by Phillips, another off his bowling - before he pulled off his moment of magic.