Joe Root and Rory Burns lay platform before New Zealand battle back

"Bat big, bat once," had been Stuart Broad's exhortation on the second evening at Hamilton, after England's frazzled batsmen had retreated to the pavilion following a torrid evening examination from New Zealand's seam attack.

Sure enough Joe Root, England's under-fire captain, lived and breathed that rallying cry in the course of a dogged and unashamedly dour unbeaten 114 from 278 balls. It was his 17th Test hundred but his first since the tour of West Indies in February, and his slowest by a country mile, but that mattered not a jot to a man who began this match having slipped out of the top ten batting rankings for the first time in five years, and whose enduring authority as a leader seems to stem entirely from his need to get back to regular run-scoring.

The manner in which Root reached his century was a microcosm of his innings as a whole. There was fluency lurking beneath his hard-pressed exterior, as shown by the sumptuous cover-drive off Neil Wagner with which he inched into the 90s, but there was desperation too, not least in the shot that took him past his milestone: a wild flap at a wide one from Wagner once again, and an under-edge past the stumps, past the keeper and away to the rope.

It had taken Root 259 balls and the best part of 80 overs to get to his hundred, but the fact that he'd got there at all was the crucial factor. While he endured, which he did right up to a premature rain-affected close, England remained in with a shout of leaving the series with an improbable share of the spoils.

For the best part of two sessions, he had been joined in deed and spirit by the steadfast Rory Burns, who contributed a century of his own in the course of a 177-run third-wicket stand that seemed, at 201 for 2 with tea looming, to have laid the platform for the sort of monolithic single innings with which New Zealand, on BJ Watling's watch, went on to win last week's first Test at Bay Oval by a canter.

But then came the wobble that England cannot entirely shake from their system at present. Burns' needless run-out, moments after bringing up his second Test century, lifted New Zealand's spirits with the new ball on the horizon, and when Ben Stokes was prised out after an innings that had arguably started too fluently for England's attritional needs, the new boy Zak Crawley was picked off without fuss by the endlessly on-it Wagner.

At 262 for 5, that left Root and Ollie Pope with a rebuilding job to do on a surface that was just beginning to misbehave, and though they survived to stumps without further alarm, the situation wasn't quite as clear-cut as England might have liked. They still trailed by 106, and with Sam Curran and Chris Woakes to come, there's still plenty chance for England to scrape together a useful lead. But whether there's now the time and the personnel to turn the screw will be another matter.

Nevertheless, the relative ease of England's progress after the drama of their 18-over prologue on the second evening was belated evidence that bowling first on this surface maybe hadn't been such a bad idea after all. There are still plenty more runs to be mined on this deck before any real demons are unearthed.

As for the tempo of England's innings, a good night's sleep clearly helped, as Root and Burns - who had been dropped twice before he had reached 20 - were given a chance to rest up after 124 arduous overs in the field. But the pitch too had reverted to type after briefly quickening up in the latter stages of New Zealand's innings, and for much of this third day, batsman error was the only real prospect of any player being dislodged.

Wagner and his left-arm bouncing bombs proved the right sort of chaos to keep England honest, as Burns in particular discovered in a range of mild alarms, including a wild bouncer that flicked his shoulder and a spliced poke that looped out of the reach of leg gully. But these moments were the exceptions rather than the rule throughout a burgeoning stand, and as both men began to gauge the lack of pace in the deck, they each began to seize on anything short.

Burns climbed into consecutive Wagner short balls to rush into the 40s, and his half-century duly arrived two balls before the drinks break, from 97 balls. Root at the other end was made to wait rather longer for his mini-landmark, but he won't have minded that, for time at the crease was every bit as important for an England captain who has been feeling the pressure like never before in the days since the Mount Maunganui rout.

The early overs of Root's innings were a battle for balance, as he challenged himself to get his feet moving in synch with the rest of his technique, but as the lunch break approached he was looking like the compact world-beater of old - even if he needed a successful review on 47 to save himself from a leg-side strangle that replays showed had clipped pad not bat.

With that alarm behind him, Root picked off another of his bread-and-butter leg-side singles to reach his fifth half-century in his last seven Tests, a stat which puts some of his recent struggles into context, even if it simultaneously reawoke that old chestnut about his inability to convert starts to finishes. Nothing less than three figures would suffice, and he knew it.

Burns at the other end did not miss out, although he should by rights have been toast on 86 when he clipped Henry to Wagner at mid-on and set off for a kamikaze single. Tom Latham, a wicketkeeper by trade, was waiting obediently at the non-strikers' end to whip off the bails, but Henry in his excitement rushed back to do the job himself, and his fumble allowed Burns to fling himself to safety.

It was the last true let-off that Burns would require in another innings, like his Ashes hundred at Edgbaston, that perhaps looked chancier on the highlights reel than it ever felt at the time. But it was not a lesson learnt, for in the very same over with which he brought up his hundred, he took on Jeet Raval's arm as he turned unwisely for a second run, and lost - though not before the third umpire Bruce Oxenford had raised his hopes of an unlikely reprieve by struggling to make out the white bails against the white shirt of the keeper Watling.

Out came Ben Stokes - and so too a set of yellow bails to guard against further third-umpire shenanigans - and out came a series of thumpingly confident strikes that hinted at a player who was still seeing the ball like a planet. And yet, with New Zealand taking the new ball in the over before tea, Stokes seemed reluctant to commit too fully to the aggression that his form seemed to warrant. It would prove his undoing when he dangled his bat to an off-stump nibbler from Tim Southee, and edged low to a tumbling Ross Taylor at a wide slip.

His departure brought Zak Crawley to the middle at an uncomfortable juncture, and his first impressions weren't entirely encouraging. He all but ran himself out in his haste to get off the mark from his fifth delivery, and one ball later he pushed with hard hands at Wagner to graze a low edge to the keeper. Such are the frailties that run deep in England's Test squad at present. All the more reason why a return to form for their classiest act is so desperately welcome.