England's first innings in Mount Maunganui was built almost single-handedly by Harry Brook, whose 135 helped them set a modest target of 224 as wickets around him tumbled.
The visitors were in early trouble thanks to New Zealand's pace attack, with Zak Foulkes (4-41) and Matt Henry (2-53) reducing England to 56-6 within the first 12 overs.
Jamie Overton added a handy 46, but it was Brook's commanding innings that kept England competitive, reaching his century with three consecutive sixes and finishing with 11 sixes in total before being dismissed while attempting a sweep off Mitch Santner.
England's innings was all over by the 36th over, however, and their total was always going to be a tough one to defend.
Chasing the target, New Zealand wobbled at times, losing four wickets - including former captain Kane Williamson for a duck - but Mitchell's unbeaten 78 anchored the innings.
Bracewell also made a valuable 51 before running himself out, while Santner contributed a quick 27 to stabilize the chase.
New Zealand eventually completed the run chase in 36.4 overs, with Bryan Mbeumo's late flourish ensuring the Black Caps emerged victorious in a hard-fought contest.
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