From 115-1, with Tammy Beaumont and Heather Knight once again well set, England couldn't build a big total. While Beaumont carried her bat, possibly too slowly, with an unbeaten 88 from 113 balls, Knight departed for 60 off 82, and nobody that followed could pass 15 as the visitors were bowled out for 220 in the 48th over.
Usually, that total would be a relatively straightforward chase, but after their performances in the first two ODIs, it was a decent challenge for the White Ferns, and another limp display looked plausible after a poor start.
Natalie Dodd's international struggles continued with a disastrous three off 19 balls, and when Hayley Jensen and Sophie Devine also departed cheaply, the White Ferns were at 51-3 after 17 overs.
This time though, their key players produced a match-winning display. Satterthwaite became the third Fern to 4000 ODI runs on her way to her seventh century, with a top-class 119 not out off 128 balls, and Kerr continued her rise as an all-rounder with an unbeaten 88-ball 72.
The pair's partnership was a fourth-wicket record for New Zealand, and despite the asking rate nearing a run-a-ball with nine overs remaining, they eventually got home comfortably with 20 balls remaining to give the Ferns a much-needed boost.
* Wellington produced a record-breaking display in the one-day Ford Trophy today.
Led by Finn Allen's absurd 128 off 59 balls and Tom Blundell's 151, Wellington produced the highest score in New Zealand one-day history, finishing at 427-8 against Otago at the Basin Reserve.
Allen, the 21-year-old phenom who shone in the Twenty20 Super Smash, tied the record for the competition's fastest 50, off 50 balls, though the innings which he now shares the record with – Peter Fulton's century – was accomplished in a one-day final that was reduced to a 20-over-a-side-affair.
Allen smashed nine fours and 11 sixes and was remarkably dismissed with 29 overs remaining, at which point Wellington had already racked up 191 runs.
Otago gave their record chase a fair shake, but were dismissed for 345 in the 42nd over.