The visitors were easing towards their target of 137 with Nat Sciver-Brunt and Heather Knight's classy stand of 57.
The White Ferns then fought back to dismiss both set batters in the 18th and 19th overs. But Sophia Dunkley held her nerve, hitting her second ball for four to win with seven balls to spare.
Earlier, the hosts slipped to 31-4 and 69-5 after choosing to bat first, but Izzy Gaze's unbeaten 51 from 28 balls led a recovery to 136-6.
Sciver-Brunt triggered the top order collapse in a hostile and disciplined opening spell with Lauren Filer, who went wicketless but troubled the inexperienced line-up with her pace and bounce.
It completed a 4-1 series win and the perfect preparation for the up-coming home series against Pakistan which begins at Edgbaston on Saturday 11 May. England Captain Heather Knight on TNT Sports: "I'm really pleased with how we started with the ball, we were aggressive and got those early wickets, so it was exciting to watch.
Player of the Match Nat Sciver-Brunt on TNT Sports: "It was great to get on a seamer-friendly wicket which we made the most of in the powerplay.
"I'd have liked to be in with Heather at the end but it was an important partnership from us to solidify the win."