Satterthwaite fought through cramps to craft an unbeaten 102 as the White Ferns pulled off the second biggest run chase in women's cricket history, recording a five-wicket win in the first clash of the three-match Rosebowl series.
Backing up from the Twenty20 series victory over their trans-Tasman rivals, a one-day series victory would be extremely significant for the White Ferns, who haven't claimed the Rosebowl since 1999.
After 14 defeats and a drawn series, it looks like that drought could soon be over if the burgeoning Kiwi side continue their excellent recent performances.
Excellency is required to topple Australia, who set the White Ferns an extremely challenging total after winning the toss and deciding to bat on the compact confines of Eden Park Outer Oval.
Australia posted 275, spearheaded by a fantastic century from Beth Mooney, who struck a career-best 100 at the top of the innings.
She was supported by valuable knocks from Rachel Haynes (50 from 61) and a maiden 43-ball fifty from Elyse Villani as Australia built towards a mammoth score.
Haynes was involved in two controversial incidents. Initially dismissed early in her innings, Haynes was recalled due to a no-ball ruling from the umpire, who incorrectly adjudged that the Ferns had set an illegal field.
Her eventual dismissal was equally controversial, with wicketkeeper Rachel Priest claiming a catch that may have bounced before it hit the gloves.
Australia kept accelerating though, and at 237-3 with eight overs to go, a total of 300 looked on the cards. However, excellent death bowling from Holly Huddleston and Lea Tahuhu restricted the visitors to 275 all out in the 49th over.
New Zealand had never chased down more than 267, but captain Suzie Bates got them off to a flying start. Bates mixed power and innovation as she raced through to 55, but was caught at point as Australia started to restrict the run rate.
Satterthwaite initially struggled for timing as the required run rate creeped towards seven an over, but influential cameos from Katey Martin (43 from 49) and Katie Perkins (29 from 27) kept the runs flowing.
Their contributions helped Satterthwaite find a rhythm, bringing up her fifty from 76 balls, and quickening when joined by Perkins. The pair added 77 from just 64 balls to reduce the asking rate to a run-a-ball, while Australia were sloppy with 16 wides and several misfields.
The requirement of 60 runs from 60 balls became 29 from 30, and then 13 from 13 as Satterthwaite started to cramp up, but by then her strokeplay was exquisitely timed.
A late cut and a one-legged pull for consecutive boundaries brought up her century (her second fifty coming from just 35 balls), and she fittingly struck the winning runs to claim a memorable victory.
The White Ferns have a chance to win the series on Thursday in Mount Maunganui.
