Having already won the ODI series 2-1, England comfortably defended a total of 128 for nine, skittling the hosts for 96 to seal a 32-run victory.
England wicketkeeper Amy Jones effected three stumpings in a superb display behind the wickets, while opening bowler Katherine Brunt was named player of the match after taking two for 19 and wrecking the home side’s top order.
The tourists struggled with the bat, scoring steadily if unspectacularly in an innings devoid of major partnerships and scores.
Number six Fran Wilson top-scored with 31 not out off 23 balls, having come to the crease at a slightly precarious 70 for four in the 12th over.
Sophia Dunkley was the only other tourist to breach 20, making 26 off 29, as New Zealand medium pacer Sophie Devine claimed three for 31.
But England’s bowlers produced a fine display, kick-started by Brunt removing openers Devine and Hayley Jenson – both lbw for a duck – in the first over.
Amy Satterthwaite and Amelia Kerr steadied the innings by adding 37 for the third wicket, before both were stumped by Jones – Satterthwaite off leg-spinner Sarah Glenn for 25 and Kerr off left-arm spinner Sophie Eccleston having made 18.
That left New Zealand 45 for four and England pressed their advantage home with five more wickets for just 18 runs.
England off-spinner Mady Villiers claimed three wickets, including Kate Ebrahim and Leigh Kasperek off successive balls, the latter becoming Jones’s third stumping.
Ecclestone bowled Kerr to leave the hosts 63 for nine, but the last-wicket pair of Maddy Green (20) and Rosemary Mair (13) provided a bit of resistance before Nat Sciver dismissed the former to wrap up the tour.
Additional reporting by PA.