England set New Zealand a formidable 382-run target in the second Test after declaring their second innings at 352 for nine on day four in Christchurch on Monday.
If New Zealand reach the target it will be the seventh-highest successful run chase in Test history.
The England declaration came as Colin de Grandhomme brought New Zealand back into the Test with his medium-paced deliveries.
Joe Root and Dawid Malan had led England to 262 for three before de Grandhomme made the breakthrough that saw six wickets fall for 90 runs on a benign wicket.
De Grandhomme finished with four for 94 as he led a New Zealand attack hampered by the unavailability of strike bowler Tim Southee who was suffering from a virus.
A New Zealand victory would see them sweep the series, while England need to come out on top to snap a 12-match away streak without a win.
England resumed the day at 202 for three and Root and Malan appeared comfortable in compiling a 97-run partnership until both fell in the space of three deliveries.
Root was out for 54 and Malan 53 as England reached 278 for five at lunch.
The New Zealand rally continued at the resumption of the middle session when de Grandhomme removed Ben Stokes for 12.
In the first ball of the following over, New Zealand appealed long and loud for Jonny Bairstow to be caught behind off Boult.
Umpire Marais Erasmus said no, New Zealand had no reviews left and the snicko technology confirmed a faint touch.
Stuart Broad reached 12 when he was caught by a diving Ish Sodhi at midwicket for de Grandhomme's third wicket. Mark Wood was bowled by de Grandhomme for nine.
Bairstow continued and when he was out for 36 to give Neil Wagner his second wicket the declaration came.