The Diamonds 47-34 victory - in front of a crowd of 10,379 at the venue for next year's Netball World Cup - was their eighth consecutive win against the Silver Ferns and 16th overall against all nations since September last year.
It's Australia's best overall winning streak since winning 20 Tests in a row between 2001-03.
Diamonds' captain Laura Geitz was named Player of the Match as Australia also held New Zealand to its lowest score in Tests between the two countries since 2009.
"I'm so proud of what we've achieved as a team and extremely proud of the girls and the way we played tonight," Geitz said.
Diamonds coach Lisa Alexander began the match with the same starting seven she's used for the series and, as they've done in the previous two Tests, Australia got away to a strong start in the opening minutes.
Slick ball movement from their mid-courters into shooters Caitlin Bassett and Natalie Medhurst saw the Diamonds lead 14-7 at quarter-time.
Silver Ferns coach Wai Taumaunu made a change to her line-up to start the second term with Grace Rasmussen replacing Liana Leota at wing attack and New Zealand enjoyed a brief period of dominance, closing to within five goals of the Diamonds.
But a 6-0 run, inspired by some great defensive work by Geitz and Julie Corletto, saw Australia race to an 11-goal lead mid-way through the quarter and they went into half-time leading 24-15.
As in Melbourne, Tegan Caldwell came into goal attack to begin the second half for Medhurst while Jodi Brown replaced Ameliaranne Wells in the same spot for the Silver Ferns.
The experienced combination allowed New Zealand to keep track with the Diamonds, but seven goals was the closest the Silver Ferns could get before Australia scored the last four goals of the term to hold a commanding 35-24 advantage heading into the last quarter.
Sharni Layton replaced Renae Hallinan at wing defence to begin the final term while Bailey Mes came on at goal shooter for the Silver Ferns with Medhurst returning to goal attack for the Diamonds after a quarter on the sideline.
After the Diamonds opened up a game-high 14-goal lead, the game was stopped after Silver Ferns captain Casey Kopua suffered a knee injury and was carried off the court and straight to the change rooms.
The loss of their captain seemed to briefly inspire the Silver Ferns before the Diamonds again powered home with the last four goals of the game.
The series now returns to New Zealand for the fourth and final Test at The Trusts Arena on Wednesday 15 October at 4.00pm (AEDT). The Constellation Cup will be presented to the Diamonds at the conclusion of that match.