Leeds - New Zealand were set a target of 468 to win the second Test at Headingley after England declared their second innings on 287 for five.
The most any side has made to win in the fourth innings of a Test is West Indies' 418 for seven against Australia at Antigua in 2002/03.
New Zealand's corresponding record is the 324 for five they made against Pakistan at Christchurch in 1993/94.
England's second innings total featured 130 from captain Alastair Cook as the opening batsman extended his England Test century record to 25.
Jonathan Bairstow was 26 not out and Matt Prior four not out when Cook declared shortly after lunch.
England lead this two-match series 1-0 after their 170-run win in the first Test at Lord's.