Browne, though, remained and with three wickets in hand needed 14 off the last over. She was then caught off the first ball, effectively ending the White Ferns' chances.
Schutt was solid, with two wickets from her 10 overs, while Perry was on target at the end of the innings when she knocked over Rachel Priest and Sara McGlashan.
Earlier, Australia again got off to a strong start and set a good platform for their middle order to build on.
A second-wicket partnership worth 58 between Rachael Haynes (32) and Jess Cameron (66) took the home side to 73 for one. It took a great piece of fielding from Katie Perkins to break the stand, with Haynes run out in the 12th over.
That brought last match's centurion Meg Lanning to the crease. Alongside Cameron, she kept the momentum for Australia and put on 58 for the third wicket.
Cameron brought up her half-century, before being dismissed by Satterthwaite in the 21st over.
The White Ferns now look towards the ICC World Cup in India, which begins late next month.