The England captain was unbeaten on 27 at Headingley — five runs short of passing mentor Graham Gooch's record of 8,900 runs. Fellow opener Adam Lyth was looking settled on 27, his highest test score.
Earlier, New Zealand resumed on 297-8 and its tailenders cut loose under blue skies, adding 53 runs in 7.1 overs.
Stuart Broad took the Black Caps' two last wickets, removing Matt Henry (27) and Trent Boult (15), for figures of 5-109 — his 13th five-wicket haul in tests.
Mark Craig was unbeaten on 41.
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