Lunch New Zealand 329 (Mitchell 109, Blundell 55, Leach 5-100) and 13 for 0 trail England 360 (Bairstow 162, Overton 97) by 18 runs

Jamie Overton‘s dream of a debut Test century was crushed by the skill of Trent Boult, but Jonny Bairstow and Stuart Broad kept the strokes flowing on another free-wheeling morning at Headingley as England – against all expectation bar their own – romped through to an eventual first-innings lead of 31, despite having slumped to 55 for 6 on the second afternoon. By lunch, New Zealand’s openers had chipped off 13 of those runs in a five-over foray.

Bairstow, 130 not out overnight, pushed on to a mighty 162 from 157 balls – the second-highest of his ten Test centuries – before holing out to long-off, but the star of England’s morning show was the long handle of Broad, who ransacked 42 runs from 36 balls, including six fours and two sixes, before New Zealand’s old firm of Boult and Tim Southee restored some late order to their toiling efforts.

Despite another morning of ceaseless entertainment from England’s batters, the one crushing disappointing for another rapt Headingley crowd was the failure of Overton to push on from his overnight 89, and become the first England player – and only the 11th in Test history – to make a century on debut from No. 8 or lower.

All the positive mental attitude in the world could not quite prepare Overton for the scenario he faced this morning, after what must surely have been a fretful night’s sleep, and with history winking at him with every delivery. Despite the best endeavours of his partner Bairstow, who kept the strike rotating to offer him every chance to find his fluency, Overton’s resumption was a comparatively tentative affair, and one that was ultimately ended – three runs shy of nirvana – by New Zealand’s most constant menace, Boult.

After throwing his hands through one cathartic square drive for his first boundary of the day, Overton chanced his arm once too often as Boult followed up with one of his classically tight-lined outswingers. A thin edge flew low to Daryl Mitchell at first slip, and as he turned to trudge back to the dressing-room, Bairstow sprinted up behind him to put an arm around his shoulder. No matter what those three runs may have meant personally, his contribution to a desperate team situation had already been invaluable.

Bairstow, whose running between the wickets had been particularly aggressive, kept his innings ticking along without having to unfurl many of his most flamboyant strokes of the second afternoon. That was largely because Broad, one day after his 36th birthday, emerged with a mood for mayhem after suffering pad-rash for the entirety of that record-breaking seventh-wicket stand of 241.

After taking seven deliveries to find his feet, Broad announced his arrival by taking on Boult head-on, with a volley of four, four, six from the first three balls of his 21st over – the latter a huge smear from the full length, high over the bowler’s head. He took a similar approach to the short balls of Neil Wagner, wiping him over midwicket as he retreated to leg in his habitual front-foot-clearing style, and after clubbing two more fours through the covers off Southee, he was eventually done in one ball later by a fine bail-trimmer, to depart at 351 for 8.

Amid all of Broad’s biffing, Bairstow arguably lost a degree of fluency, as well as much of the strike. He had brought up England’s second-fastest 150, from 144 balls, with a punch into the covers off Wagner, but he faced just 13 more balls in the next nine overs, including a tough caught-and-bowled chance to the spinner Michael Bracewell, before a huge hack down the ground to long-off, where Boult made excellent ground to cling onto a sprawling chance.

Jack Leach had time to extend England’s lead still further with back-to-back boundaries from his first two balls, but after Southee struck for the second time, there wasn’t much rest in store for Bairstow. With Ben Foakes reporting a stiff back, he was handed back the wicketkeeping duties for the start of New Zealand’s second innings, and almost immediately found himself standing up to the stumps, as Leach was handed the new ball in a two-over experiment, the first time a spinner had done so in England since Graeme Swann at Lord’s in 2009.

Andrew Miller is UK editor of ESPNcricinfo. @miller_cricket