After the women defeated the United States 24-7 at HBF Park to book a final showdown with Ireland, the men beat Fiji 22-7.
They will face series-leaders Argentina, who beat them in the final of the last tournament in Cape Town.
Both Australian teams will be looking to win a final on home soil for the first time since triumphing in Sydney in 2018.
In the men's semis, a perfectly timed pass from Maurice Longbottom sent captain Nick Malouf charging to the line for Australia's first try.
Fiji retaliated immediately with a brilliant long-distance team with Josev Talacolo going over to lock the teams at 7-7 at half-time.
Two massive tackles forced Fiji back and pressured them into conceding a penalty close to their posts, with Longbottom opting to kick for goal.
He kicked the penalty and Henry Palmer crossed in the last two seconds to seal an impressive victory for a team that has lifted in the knockout games after losing two of their three pool matches.
They will start as underdogs as Argentina continued their red-hot form with a convincing 24-5 win over Ireland.
In the men's classification matches, New Zealand took ninth with a 21-14 victory over Samoa while Great Britain beat Canada 17-5 in the 11th-12th place playoff.
The women cruised through to their final despite missing three key players.
Australia were without suspended siblings Maddison and Teagan Levi, while in-form Bienne Terita was helped off the ground after just two minutes.
Teagan Levi will be available for the final later on Sunday.
The hosts took five minutes to prise open the USA defence with Madison Ashby setting up Alysia Lefau-Fakaosilea after Australia swooped on a loose American lineout throw.
Sharni Smale crossed just before half-time and Australia led 12-0 at the break.
A long-distance try early in the second half to Dominique du Toit pushed Australia clear.
The USA scored a try but Kaitlin Shave notched a final five-pointer for the home team.
Ireland thumped Great Britain 31-7 in the other semi.
In the early rankings games, Brazil defeated South Africa 7-0 in the ninth-10th playoff and Japan beat Spain 33-5 in the battle for 11th and 12th.
15°C