Jofra Archer represents a potentially transformative new weapon for Joe Root and one that could help his England side overcome flat pitches on foreign soil with the Kookaburra ball.

But to watch Root deploy Archer on day three in Mount Maunganui, as BJ Watling’s belligerent unbeaten century ground the tourists into the dirt, was to wonder whether the captain is still wrestling with the instruction manual.

Watling, it must be said, produced a wonderful exhibition in restraint and bloody-mindedness. He walked off at the end of the third evening with 119 runs from 298 balls, having batted through all three sessions to move New Zealand from their overnight 144 for four to 394 for six and a precious lead of 41.

It was the eighth time in a 64-cap Test career that the 34-year-old has brought up three figures and, with 217 dismissals, he has long been a wicketkeeper-batsman of some distinction, even if it sometimes takes a while for his name to emerge when world XIs are being debated in the pub (or not at all when the ICC are doing theirs).

Watling described himself as a “limited” batsman afterwards in typical self-effacing Kiwi fashion. Yet has been the bedrock for stands of 119 with Colin de Grandhomme – the all-rounder continuing a fine match with 65 from 108 balls – and then an unbroken one of 78 runs with Mitch Santner, who in just over two hours showed courage under fire as Ben Stokes and Archer went hard at him late on.

But as Watling whittled away – and what follows is not to detract from his innings of 15 fours, chiefly struck square but with two sumptuous straight drives – the question of England’s overseas impotence re-emerged.

After Sam Curran extracted capricious bounce to remove Kane Williamson on day two, he struggled for impact as the pitch turned flat. Stuart Broad was miserly, going at under two runs an over, but he only occasionally beat the bat, while Jack Leach produced just a couple of spiteful deliveries.

Most puzzling on a day of perspiration, when just two wickets fell, both reviews were burned, players groused over misfields and the travelling supporters tried – but failed – to inspire the troops was Root’s use of his two faster bowlers.

Archer first, who Root twice ignored at times when he might have expected to bowl. The first came at the outset when Henry Nicholls was alongside Watling. The left-hander had to pass a concussion test before play, having been struck in the head by Archer the evening before, so why not resume hostilities?

And then after lunch, with the new ball taken and de Grandhomme still in the foothills of his innings, Root instead turned to Curran and Broad. When the all-rounder comfortably drove the former for a couple of meaty fours, his innings was suddenly up and away again.

Having been given out lbw off the bowling of Jofra Archer, right, BJ Watling successfully reviews the umpire’s decision. Photograph: Michael Bradley/AFP via Getty Images

As well as forcing Jos Buttler to leap around, in a tough outing for England’s returning wicketkeeper overall, there was some heat within Archer’s three spells. His afternoon burst even soared past 90mph but Watling and de Grandhomme held firm, the latter even taking on the short ball.

Root seemed only interested in using the 24-year-old as a battering ram, however, and the pair did not always appear aligned here. The two times Archer nearly burst through Watling’s defence came with the fuller ball: a reviewed lbw shout shown to be missing by millimetres on height and a later inswinger, this time given out on the field, overturned due to a faint inside edge.

“He’s still very young in his Test career,” said Chris Silverwood, the head coach, after stumps. “Jofra’s learning about himself and the game of Test cricket. And, equally, Joe is learning to captain him as well. From a holistic point of view we’re growing together, really.”

And then there was Stokes, who bowled just four overs before lunch and then wasn’t seen at all during a wicketless afternoon of 92 runs. When he emerged after tea to remove de Grandhomme with his first loosener – Dom Sibley taking a spectacular diving catch to his right – it at least answered the question about a possible injury niggle.

Sibley, the only person in Bay Oval to consider it cable-knit weather, was stationed at gully when the ball stuck in his bear paw. This was only because Rory Burns was off the field having some split webbing in his hand glued back together after a quarter-chance off de Grandhomme’s blade inflicted the wound.

Had Stokes’s hands been as adhesive as Sibley’s (rather than Burns), Watling’s innings would have ended on 31 during the ominously sleepy morning session. The all-rounder put down a catch at slip off the bowling of Root, who at least trapped Nicholls lbw for two balls later.

This drop by Stokes had come just moments after being heard barking “this is a Test match” at Archer in response to a sloppy misfield. The testy little vignette encapsulated England’s mood all day as Watling, the man to pinch the extra run, delivered a how-to manual in the art of dogged defence.