Daryl Mitchell and Tom Blundell ended day three at Headingley tasked with producing another defiant partnership to put New Zealand in a winning position after England seemingly tilted the balance of a fascinating third Test slightly in their favour.
Seeking a 3-0 whitewash with victory at Headingley, England resumed play on the third day hopeful Jonny Bairstow and Jamie Overton would steer them into a first-innings lead.
Bairstow added to his overnight 130 to go past 150 in expedient fashion and, though Overton (97) was denied a Test century on debut, England claimed a lead of 31 runs as they were bowled out for 360.
Tom Latham (76) produced his best batting effort of a difficult series, but New Zealand slumped from 152-2 to 168-5 after a rain break in the evening session to leave Mitchell and Blundell nursing a lead of 137 when rain stopped play.
Bairstow was fluent once more after the morning session got going, his 150 the second-fastest in England's Test history as it came in 144 balls.
Overton was evidently more nervous and his hopes of a hundred went when he chased an off-stump delivery from Trent Boult and edged to first slip.
Stuart Broad (42) hit a barrage of boundaries to help England beyond 350 before he and Bairstow went in successive balls, Jack Leach the last man to depart after a pair of fours.
Despite Will Young's early exit to Matthew Potts (2-20), New Zealand progressed serenely until the first ball after tea, when Overton had Latham caught behind.
A brief rain delay undid New Zealand further. Ollie Pope claimed a brilliant catch at short leg as Devon Conway fell to Joe Root and Potts drew an edge to remove captain Kane Williamson (48), with Ben Stokes' faith in Leach rewarded by the spinner dismissing Henry Nicholls (7) caught and bowled and giving Mitchell and Blundell a recovery mission.
Quick work for Bairstow
Bairstow, who finished with 162 from 157 balls, was the star of the show with the bat at his home ground in England's first innings.
He did most of the damage on day two but only Stokes, who did so in 135 balls against South Africa in 2016, can claim to have reached a Test 150 faster than Bairstow, who donned the wicket-keeping gloves for New Zealand's second innings due to a back problem for Ben Foakes.
Can New Zealand's dream team do it again?
Mitchell and Blundell combined for a stand of 195 in the first Test and 236 in the second. They will likely need to produce another fine partnership to help New Zealand post an imposing target for England.
Potts, who has now dismissed Williamson in three of the Black Caps skipper's four innings this series, looks in the kind of form to thwart them.