Captain Alastair Cook and Adam Lyth were both 15 not out at the interval, having negotiated nine overs without undue alarm after New Zealand declared their second innings on 454 for eight.
Resuming on 338 for six, the touring side plundered 116 runs in 75 minutes at Headingley to close on a series-levelling victory.
BJ Watling was caught at third slip by Joe Root off James Anderson for 120 before Mark Craig and Tim Southee added 67 runs off 53 balls.
Southee, on 40, hit spinner Moeen Ali straight to Anderson at long-off but Craig continued to flay the England attack on the way to an unbeaten 58.
Stuart Broad conceded 20 runs off one over and the England fast bowler was hammered for three more sixes in the final over before the declaration.
England won the first Test at Lord's by 124 runs.
The highest successful fourth-innings run chase in tests was achieved by West Indies who made 418 for seven to beat Australia in Antigua in 2002-03. – Reuters
Original source: England off to steady start