Player of the series Sarah Taylor hit 93, from 99 balls, before Natalie Sciver’s unbeaten 65 steered England home with five overs to spare.
New Zealand had posted 230 for eight on the back of Katie Perkins’ 70 not out. Becky Grundy claimed three for 36 while Laura Marsh and Kate Cross chipped in with two wickets apiece.
England were 70 for three in reply, after skipper Charlotte Edwards was trapped lbw for 20, but Taylor took charge and was on course for a century until she was run out.
Sciver finished the job by clubbing a four to the midwicket rope to secure the series 3-2. England won the Twenty20 series 2-1 earlier this week.