A Tom Blundell century for New Zealand and two late England batting stumbles left the first Test tantalisingly poised at Mount Maunganui on Friday.
The tourists held a 98-run lead with eight second-innings wickets in hand and still three days to play in a fast-moving day-night Test at the Bay Oval.
Blundell's career-best 138 steered his side to 306 and just 19 runs short of England's 325-9 declared. The delicate nature of the contest didn't prevent the tourists playing their shots, although they lost openers Ben Duckett, for 25, and Zak Crawley, for 28, in reaching 79-2 off 16 overs.
England's best bowler, Ollie Robinson (4-54), said the honours were "pretty even in the end" after his side dominated day one with their aggressive batting before reducing the Black Caps to 37-3.