Openers Tom Latham and Devon Conway scored unbeaten half-centuries to give New Zealand a foothold in the second Test after England enforced the follow-on in Wellington on Sunday.
The Black Caps unveiled some much-needed combative qualities in a series dominated by the tourists, reaching 128 without loss at tea on day three at the Basin Reserve.
England are still well placed to push for victory and secure a 2-0 series sweep after posting a 267-run first Test win at Mount Maunganui.
New Zealand have opened up the rare prospect of winning after following-on, something achieved only three times in Test history.
That looked a distant prospect when dismissed for 209 in their first innings midway through the morning session, 226 runs behind England's 435-8 declared.
Compact left-handers Latham and Conway negotiated 19 overs before lunch to be 40-0 and conditions flattened out nicely in the afternoon.
England's attack had few answers to the pair, whose concentration and technique were a level above three fragile New Zealand top-order efforts earlier in the series.
Conway's outside edge was beaten on several occasions but he held his nerve and found the boundary seven times, including a six off spinner Jack Leach.
Their orthodox batting was a contrast to a lively first hour's play, when New Zealand lost their last three first-innings wickets for 71 runs off just 11.2 overs.
Seamer Stuart Broad claimed all three wickets to finish with 4-61, his introduction halting a New Zealand charge led by Tim Southee.
The New Zealand captain was dismissed for 73 after blazing 50 runs off 30 balls on Sunday morning, his free-wheeling knock laced with six sixes, including three from one Leach over.
Southee finished four runs short of his career-best score, achieved in his Test debut 15 years ago.
His dismissal was followed quickly by those of Tom Blundell for 38 and Matt Henry for six, prompting England captain Ben Stokes to enforce the follow-on.