England captain Alastair Cook was 88 not out and Jonathan Trott 11 not out at Headingley.
Earlier, New Zealand were dismissed for 174 in reply to England's first innings 354 -- a deficit of 180 runs.
Although New Zealand were short of the follow-on avoidance target of 205, Cook decided against making the tourists bat again.
Off-spinner Graeme Swann took four for 42 and fast bowler Steven Finn three for 36 as New Zealand suffered a second straight top-order collapse after being skittled out for 68 in the second innings of England's 170-run first Test win at Lord's last week.
New Zealand left-arm quick Trent Boult took five for 57 in an England first innings featuring Joe Root's maiden Test hundred.
England lead the two-match series 1-0.