New Zealand's top order unearthed some tenacity to close within 24 runs of England in their second innings on Sunday and set up an absorbing last two days of the second Test in Wellington.
The hosts were 202-3 at stumps on day three, their gritty response after being asked to follow on founded on half-centuries by openers Tom Latham and Devon Conway.
Kane Williamson was a patient 25 not out at the close, needing just four more runs to surpass Ross Taylor as New Zealand's greatest Test run-scorer.
The former skipper will resume on Monday alongside Henry Nicholls (18 not out) with New Zealand harbouring slim hopes of squaring the two-match series on a Basin Reserve pitch starting to offer turn and variable bounce.
Only England (twice) and India have achieved the feat of winning a Test after following on.
A New Zealand victory 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.
Latham (83) and Conway (61) combined to frustrate England for 149 runs before the first wicket fell, unveiling some much-needed combative qualities in a series dominated by England's impressive seam bowling and some fragile Black Caps top-order batting.
New Zealand's foothold in the game loosened when both openers and Will Young (8) fell in the space of 18 runs, all to spin, to leave them 167-3 before Williamson and Nicholls dug in.
Jack Leach was the pick of England's attack, taking 2-59 off 31 overs, with his ball to bowl Young a textbook delivery for a left-arm spinner.
Part-time tweaker Joe Root also found turn, trapping Latham lbw from a rare loose in the opener's 172 balls at the crease.
England are still well placed to notch a seventh straight Test win and secure a 2-0 series sweep after their 267-run first Test triumph at Mount Maunganui.
The key will be removing Williamson, who has been well short of his best form in the series, tallying 10 runs in three previous innings.
However, the 32-year-old unleashed a typically frill-free knock, taking few risks in his 81 balls faced to keep his side in the contest.
Four more runs will carry him past the New Zealand record of 7,683 runs scored by long-time team-mate Taylor, who retired last year.
A grinding finish to the day was in contrast to a lively first hour, 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.