Peter Fulton became the fourth New Zealand batsman to score a century in each innings of a test as the hosts set England an improbable victory target of 481 when they declared their second innings closed after lunch on the fourth day on Monday.
Fulton, who brought up his century with a glorious straight six off Stuart Broad, was caught on the boundary by Joe Root for 110, following his 136 in the first innings.
New Zealand captain Brendon McCullum was 67 not out, his third half century of the series and seventh in nine innings in all forms of cricket against the tourists, when he declared at 241 for six about 45 minutes into the middle session.
England would need to break the world record for the highest successful run chase to win the match, and series. The highest fourth innings score to win a game was the 418 for seven West Indies scored against Australia in 2003.