England's Jonny Bairstow (73) had earlier hit his fastest half-century in T20 internationals as the hosts set New Zealand a target of 176 after finishing on 175-8 on a warm evening in Nottingham.
New Zealand won with 2.4 overs to spare, finishing on 179-4 with Mark Chapman 40 not out.
England had won the first two matches, with New Zealand coming back strongly to end on level terms.