Seamer Gus Atkinson took a hattrick to skittle New Zealand's tail Saturday before England's batters powered them more than 200 runs ahead in the second Test.
The tourists were on top at lunch on day two in Wellington, coasting to 82-1 in their second innings after claiming five wickets inside the first 40 minutes to dismiss New Zealand for 125.
England's overall advantage grew from 155 to 237 thanks to some clean striking from Ben Duckett (39 not out) and Jacob Bethell (34 not out).
The only wicket was Zac Crawley, caught at midwicket off Matt Henry for eight to continue his lean series.
In 19 Test innings against the Black Caps, the opener has scored 193 runs at an average of just 10.15.
The setback didn't stymie Duckett and Bethell, whose stand had reached 73 off 82 balls, with both intent on making amends after departing cheaply in England's first innings of 280.
Earlier, Atkinson removed the last three New Zealand batters in successive balls to become the first England player in seven years to claim a Test hat-trick.
The seamer bowled Nathan Smith for 14 before Matt Henry was caught behind and Tim Southee trapped LBW - both from the only balls they faced.
The five morning wickets were shared between Atkinson (4-31) and fellow-seamer Brydon Carse (4-46) while New Zealand added 39 runs to their overnight score of 86-5.
The two overnight batsmen were quickly removed by Carse.
Blundell was bowled for 16 before nightwatchman Will O'Rourke was out LBW for a 26-ball duck.
