Gus Atkinson took a hat-trick to dismiss New Zealand for 125 and give England a first-innings lead of 155 as the tourists took full control of the second test early on the second day in Wellington on Saturday.
After the cheap loss of opener Zak Crawley, Ben Duckett and Jacob Bethell drove home England's advantage by moving to 82 for one at the lunch break at Basin Reserve to take the lead to 237.
Duckett will resume on 39 not out and Bethell unbeaten on 34, but the first session belonged to Atkinson and his fellow seamer Brydon Carse, who are both in the first few months of their test careers.
The Black Caps started the day in a hole with 86-5 on the board in reply to England's 280 and Carse (4-46) quickly made their situation worse by sending back Tom Blundell for 16 with a peach of a delivery that took off the top of the off stump.
Nighwatchman Will O'Rourke followed lbw for a duck two balls later to reduce New Zealand to 96-7 before Atkinson (4-31) took over to finish the job from the other end.
Nathan Smith had 14 runs on the board when he tried to leave a delivery only to play-on, Matt Henry was served up a fizzing bouncer, which he diverted to Ben Duckett at gully for a golden duck, and Tim Southee was trapped plumb lbw first ball.
It was the 47th hat-trick in 147 years of test cricket, the first since 2021, and the first by an England bowler since spinner Moeen Ali achieved the feat against South Africa at the Oval in 2017.
England won the first test by eight wickets in Christchurch last week and the Black Caps will have to produce something special to deny them a first series win in New Zealand since 2008 before the third and final test in Hamilton.