The Opals found it especially hard, particularly from long-range, as the Tall Ferns dictated the pace and stepped it up in defence.
Their first four points all came via free-throws, and it took more than three minutes to land any from the field.
It was a tough and defence-dominated opening quarter, which ended level at 14-14.
But the experience of Hodges, Batkovic and Jarry lifted Australia in the second term for a 40-33 lead at the main break.
Their high-energy continued into the third quarter and the Tall Ferns felt it, committing four fouls in the opening minutes.
The momentum swung entirely the visitors' way after that, with the green and gold flexing their muscle and showing why they are ranked No.2 in the world.
Hodges sealed the victory with the last five points.
The Opals have now won every Oceania series since 1974, and are on their way to a sixth successive Olympics.
They've won a medal at every Games since Atlanta in 1996, including three silver and two bronze.
But legend Lauren Jackson said she believed Australia were better placed than ever to go one better and win gold at Rio.
"I've been in championship teams my whole career ... and you have this feeling going into it, this air of success," the four-time Olympian told AAP.
"I feel like at the moment, we have that.
"I really believe that we can do something special in Rio - we could win a gold medal, absolutely. "Whether I'm on the team or not, they have probably the best opportunity they've ever had to win that gold - especially if Liz (Cambage) is healthy and fit.
"I'm really excited."
The Tall Ferns will get a second chance at qualifying in a repechage tournament involving 12 teams in June next year, with the top five earning a spot.
- AAP
