England started the day on 354-7, and Boult took two quick wickets, inducing edges by Moeen Ali on 58, and Stuart Broad on 3, for catches behind the wickets.
Mark Wood, England's new seamer, was joined by James Anderson, and they frustrated New Zealand for six overs, scoring 21 runs, until Anderson was caught and bowled in Henry's first over after replacing the loose Tim Southee.
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Anderson was out for 11, leaving Wood on 8.
Henry, in his first innings for New Zealand, took 4-93, and Boult finished with 4-79.
