Engand batters Jacob Bethell and Ben Duckett have both fallen painfully short of centuries, but their 187-run partnership has carried their team well clear of New Zealand in the second Test at Wellington's Basin Reserve.

The tourists have arrived at stumps on the second day at 378/5 in their second innings, extending their overall advantage over the Black Caps to 533 runs.

New Zealand have never scored more than 451 runs in the fourth innings of a Test.

Bethell achieved his highest first-class score of 96, before he was caught behind by wicketkeeper Tom Blundell, off the bowling of Tim Southee. Four overs later, Duckett played Southee onto his stumps for 92, giving the veteran bowler some joy in his final Test at the iconic international venue.

First-innings centurion Harry Brook reached another fifty, before he departed off the bowling of allrounder Glenn Phillips, while England's highest-ever runscorer, Joe Root (73no), and captain Ben Stokes (35no) were unbeaten at the close of play.

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But the English batters had already done the damage. (Source: TVNZ)

Earlier, fast bowler Gus Atkinson rocked New Zealand with his first Test hat-trick, as the home side's hopes of victory begin to disappear over the horizon.

Resuming the second day at 86/5, the Black Caps lasted less than nine additional overs into the morning session, losing the remaining five wickets for 39 runs, as they were dismissed for 125 - still 155 runs behind their rivals' first innings.

Three of those wickets fell at 125, as Nathan Smith, Matt Heny and Southee succumbed to Atkinson in consecutive balls, leaving Phillips not out on 16.

The Englishman became the first bowler to take a Test hat-trick at the iconic international venue.

England's Gus Atkinson on the first day of the second cricket test between New Zealand and England at the Basin Reserve, Wellington, New Zealand. (Source: Photosport)

Opting to bat again, the tourist reached 82/1 by lunch, scoring at more than five runs an over to stretch their lead to 237 runs.

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New Zealand's only sniff of success in the morning came when opener Zak Crawley continued his lean run of form, scoring 26 runs in his last four innings against the Black Cap, caught by Devon Conway off Matt Henry's bowling. Henry celebrated Crawley's scalp for the fourth time this series.

England already have a lead in the three-match series, after their comprehensive eight-wicket win at Christchurch.

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England 280 & 378/5/5 (Duckett 92, Bethell 96; Henry 2/76, Southee 2/72) NZ 125 (Williamson 37, Latham 17; Atkinson 4/32, Carse 4/46).

England lead by 533 runs at stumps on day two.