Christopher Bausor put Australia 2-0 with a long range breakout.
After Russell had raised Black Sticks hopes, Jeremy Hayward shut the door on New Zealand inside the last two minutes.
New Zealand also lost the round robin game to the Australians 3-1, but a draw against world No 14 Malaysia and dramatic 3-2 win over No 6 India got the eighth-ranked Black Sticks into the final.
Last weekend, New Zealand beat Australia 2-1 for their first win over the Australians in New Zealand since 1967.
Australia have won the other four clashes between the transtasman rivals this year, including at the Rio Olympics and the Azlan Shah tournament in Malaysia in April.
Black Sticks coach Colin Batch said while the final result was disappointing but there have been many positives that have come out of the series.
"It's obviously disappointing to lose a final like that," Batch said. ''We fought very hard in the second half to get back into it and were in a position there where we could've levelled the game.
"Overall I'm pleased with the new guys in the squad, they've experienced some high quality games both here in Melbourne and at the Trans-Tasman Trophy (in Auckland earlier this month).
"It was really important we made the final, and also our win over India which was virtually their Olympic team was pleasing so we head home with some positives to build on."
