The hosts were bowled out during the middle session on the second day after Ross Taylor scored his maiden Test century, captain Daniel Vettori made a handy 88, opener Jamie How scored 92 and Brendon McCullum chipped in with 51 from 55 deliveries.
The pair came together with the score on 277 for 6 late on the first day and dominated the first session on day two as Taylor reached his century with a hook off Steve Harmison, propelling New Zealand to 387 for 6 at lunch.
" ...it was good to silence a few people who doubted me and whether I was good enough to play at this level."
Taylor moved to 120 after lunch, but played a rare false shot, slog-sweeping at part-time off-spinner Kevin Pietersen's second ball and top-edging a catch back to the bowler, who claimed his third Test wicket.
The 23-year-old Central Districts batsman came to the crease at Seddon Park as his Test statistics were announced to the crowd over the loudspeaker system.
They were hardly endearing, as it emerged that playing his third Test, he had previously scored just 44 runs in his four innings with a top score of 17.
Loudspeaker motivates Taylor
"I heard it and I used it as motivation," Taylor told reporters.
"Seventeen is not a very good personal best score but that was definitely my motivation.
"I got off to a bit of a shaky start in my first four digs in Test cricket so it was good to silence a few people who doubted me and whether I was good enough to play at this level."
Vettori then appeared to be in sight of his third Test century, but played a lazy shot to a wide Paul Collingwood delivery and was well caught by Strauss in the slips.
Ryan Sidebottom, the most successful of the England bowlers with figures of 4 for 90, will be on a hat-trick when New Zealand bat again after capturing Jeetan Patel (5) and Martin (0) in successive deliveries to close the innings.
England stumble late
Sidebottom praised Taylor's batting but was disappointed at the way he had bowled early on the second day.
"Me and Hoggy (Matthew Hoggard) were stupidly searching for wickets this morning, rather than doing what we did yesterday," said Sidebottom.
"We were trying to bowl too quick instead of plugging away... putting he ball on an off-stump line and trying to make them play.
|"They scored 100 more than we expected."|
"I'm disappointed that we didn't bowl as well as we did yesterday. We were fired up to get the four wickets and just kept plugging away.
"They scored 100 more than we expected."
Alastair Cook and Vaughan, England's openers, began the chase slowly and made it through to 84 without loss before Cook lost concentration with less than five overs remaining in the day as he skied a catch off Martin to substitute fielder Nick Horsley for 38.
Matthew Hoggard, coming in as night watchman, was dismissed for two when he edged to Stephen Fleming in the slips in Martin's next over.
Vaughan was lucky to still be at the crease after a confident LBW appeal from Vettori, as television replays showed he was struck on the pad before the ball ricocheted on to his bat.
New Zealand's dual spin attack could pose problems for England on the fourth and fifth days, with off-spinner Patel already extracting considerable turn and sharp bounce.