New Zealand 278 (Watling 85, de Grandhomme 72, Broad 6-54, Anderson 4-76) and 42 for 0 (Latham 25*) need another 340 runs to beat England 307 (Bairstow 101, Wood 52, Southee 6-62, Boult 4-87) and 352 for 9 dec (Vince 76, Stoneman 60)
Christchurch: England set New Zealand a daunting 382 for victory on the fourth day of the second Test in Christchurch on Monday.
Resuming on 202-3, Joe Root (54) and Dawid Malan (53) played patiently but fell to the old ball in an attritional morning session at the Hagley Oval.
England's lower order, led by Jonny Bairstow's 36, hit out after lunch to help the visitors declare on 352-9.
However, Tom Latham (25) and Jeet Raval (17) guided the Black Caps to 42-0 before bad light ended play early.
New Zealand, who have a 1-0 series lead, will require their highest Test run chase if they are to consign England to their sixth loss in their past seven Tests.
Their previous highest fourth-innings chase is 324-5, which they made against Pakistan in 1994.
Joe Root's side will be looking to end a difficult winter on a positive note while the hosts, who need another 340 runs to win, are aiming for their first home series win over England since 1983-84.
After a winter that has included a 4-0 Ashes defeat and a dreadful batting performance in Auckland, England found themselves in the rare position of setting a commanding total away from home.
Root notched his seventh half-century of the winter, followed closely by Malan, and batting appeared easy as captain Kane Williamson delayed taking the new ball.
However, Malan slapped a Colin de Grandhomme delivery straight to mid-wicket before Root once again failed to build on a promising start as he flashed at the same bowler and nicked the ball through to wicketkeeper BJ Watling.