Hannah Rowe of New Zealand celebrates taking a wicket, England, 2024. Photo: PHOTOSPORT
The White Ferns have been swept in the ODI series in England, but the tourists did put up more of a fight in the third and final game in Bristol.
England won by five wickets, chasing down a target of 212 in a rain-reduced 42 overs.
The match was delayed for 95 minutes before England won the toss and for the third time in the series New Zealand batted first.
New Zealand scored 211/8 from their 42 overs with Amelia Kerr top scoring with 57.
Suzie Bates made 24, while Kerr and captain Sophie Devine (43) put on 68 runs for the third wicket.
31 from Brooke Halliday and 14 from Lauren Down got the Ferns over 200 for the first time in the series.
Lauren Bell took her maiden five wicket haul for England, finishing with 5-37.
In reply Hannah Rowe grabbed the wicket of Tammy Beaumont in the first over.
Rowe also picked up the wicket of captain Heather Knight for 9 as the home side slipped to 33 for three in the eighth over.
However Nat Sciver-Brunt and Amy Jones put on 90 runs for the fifth wicket.
Melie Kerr of New Zealand batting against England, 2024. Photo: PHOTOSPORT
Sciver-Brunt finished unbeaten on 76, while Jones made 50.
Hannah Rowe finished with two wickets, while Molly Penfold, Amelia Kerr and Brooke Halliday got one each.
Rowe and Eden Carson came into the side for Jess Kerr and Fran Jonas.
England won the first match by nine wickets and the second by eight wickets.
The two sides now meet in five T20 internationals with the first in Southampton on Sunday.