Satterthwaite made use of three dropped catches by the Australian fielders to finish on 85 off 117 balls, with just two boundaries and one six testimony to her ability to rotate the strike and find gaps in the outfield.
The White Ferns innings was based on three significant partnerships involving Satterthwaite.
She put on 87 with wicketkeeper Katey Martin for the third wicket, with Martin making a hard-hit 43 off just 51 balls, and 40 for the second wicket with captain Suzie Bates who was out stumped for 35. Katie Perkins made a belligerent 38 off 36 balls in a partnership of 63 with Satterthwaite for the fifth wicket.
Australia gifted the White Ferns 20 extras, including a whopping 16 wides.
Australian captain Meg Lanning as always was the key wicket.
She is the best women's player in world cricket with an ODI batting average of 50 and strike rate just under 100 from 55 games.
She arrived in the seventh over at 22-1 and with opener Beth Mooney laid siege on the bowling, upping the run rate to be 84-1 after 16 overs. At the same stage the White Ferns were 55/2.
At drinks Australia were well ahead on 94-1 off 16 overs before 16-year-old Wellington schoolgirl Amelia Kerr struck. She slipped a leg spinner through Lanning's defences to bowl her for 44 and then bowled Elyse Villani first ball to be on a hat-trick.
Mooney continued on past 50 before Kerr bowled her as well to leave Australia 138-4 in the 27th over.
But that was as close as the Kiwis got as the experienced Alex Blackwell (65) in her 132nd ODI and Alyssa Healy (36) shared a fifth-wicket partnership of 81 that won the match.
Kerr finished with four wickets in another top-class spell of leg spin bowling.
The deciding game is at Bay Oval on Sunday from 11am. Free entry.
White Ferns 250-8 (Amy Satterthwaite 85, Katey Martin 43, Katie Perkins 38, Suzie Bates 35; Amanda Wellington 3-50) lost to Australia 256-6 (Alex Blackwell 65, Beth Mooney 57, Meg Lanning 44; Amelia Kerr 4-54, Anna Peterson 1-27)