After the visitors claimed both opening-day singles matches at Melbourne's John Cain Arena, new British doubles pairing Jodie Burrage and Harriet Dart completed a 3-0 rout in the best-of-five qualifying tie on Saturday.
Their 6-3 6-4 win over Storm Hunter and Ellen Perez gave Great Britain an unassailable lead, sending last year's semi-finalists back to September's Finals in China.
It is the second straight year Australia have missed the eight-nation Finals.
Playing together for the first time, Burrage and Dart recovered from an early break against their experienced opponents and reeled off five straight games to claim the first set.
A see-sawing second set could have gone either way before Burrage eventually held serve to seal the result.
"We knew it was going to be an incredibly tough match," Dart told Nine post-match.
"They're two great players and they play a lot of doubles, and it was our first time playing together.
"It's a bit crazy actually because we played pretty well, didn't we? But it's such an honour to represent GB and to be able to make the finals as well is kind of surreal."
Australia had gone into the tie as strong favourites against a Great Britain team missing their four best players, with three of those opting to focus on the European clay-court swing.
But rankings counted for little as Dart led the British charge.
The world No.173 upset Kimberly Birrell 4-6 6-3 6-3 in their singles clash on Friday, building on 17-year-old debutant Mika Stojsavljevic's shock 7-6 (7-4) 7-5 win over Talia Gibson.
Big-serving Stojsavljevic arrived in Melbourne ranked 219 places below world No.56 Gibson, who had knocked off five top-20 opponents in a sparkling run of form in the lead-up.
At 2-0 down, Australia had the weight of history against them on Saturday.
Only nine teams have ever come back from 2-0 down to win since the best-of-five format was introduced in the BJK Cup - formerly known as the Federation Cup - in 1995.
The task proved too tough for the Australians as Burrage and Dart finished the job.
Australian rising star Emerson Jones was called up to take on Katie Swan in a dead-rubber singles match on her BJK Cup debut.
The 17-year-old, ranked No.134 in the world, replaced Maya Joint in the squad after the top-ranked Australian pulled out with a back injury.
10°C