Satterthwaite took the remarkable figures of 6-17 from four overs as the home side crumbled to 112 all-out in 18 overs chasing the Kiwis’ score of 150 which included 32 from Suzie Bates and 44 from Sara McGlashan.
New Zealand chose to bat first after winning the toss and Bates and Rachel Priest added 44 before Lynsey Askew trapped the latter lbw for 18.
England gave a debut to off-spinner Charlotte Russell who finished with figures of 0-26 while Jenny Gunn was the standout bowler with 2-25.
When England replied Sarah Taylor (23) and Gunn added 40 for the first wicket but Gunn (29) became Satterthwaite’s second victim with the score on 63.
Lydia Greenway contributed 29 but wickets fell at regular intervals as England fell well short in a series they had already won having taken the first two matches.
The two sides will meet on Friday in the first match of the six-match NatWest Series.