The men won their first trophy since November 2022 in Hong Kong when they overcame South Africa 26-19 in a sweltering Estadio Jose Zorrilla, with The Blitzboks having a last-gasp try ruled out by a forward pass.
And the women's team comfortably handled the United States 27-14 in their final after finally stopping arch-rivals New Zealand in the semifinals.
New Zealand had won the last five tournaments since February, beating Australia in the final every time.
Tim Walsh's side even won without two of their best players in Spain with Maddison Levi and Tia Hinds, who were missing through injury, and now take a two-point lead over New Zealand into the world championship decider next weekend in Bordeaux, France.
It was a first title double for the Aussie teams since 2018 in Sydney.
The men's victory was perhaps the bigger surprise. Even though they overcame South Africa 24-14 in pool play on Saturday, the Aussies were still underdogs in the final.
South Africa made an ominous 14-0 start through converted tries by Shilton van Wyk and Sebastiaan Jobb.
But by half-time the score was level after Australia scored on both wings through James Turner and Ethan McFarland, who broke through two defenders each.
To start the second half, Australia captain Henry Hutchison made a try-saving tackle on Tristan Leyds, who was then sin-binned for a cynical foul.
In his two-minute absence, Liam Barry's side romped ahead 26-14 after tries by Ben Dowling and Hutchison, the latter after a spectacular restart catch by a leaping Aden Ekanayake above his head.
But then Turner was red-carded for a high tackle with about 90 seconds left. South Africa rallied with a try by Gino Cupido, who then offloaded to van Wyk for what appeared to be the try forcing extra time. But the try was scrubbed after video replay showed Cupido's pass was forward.
South Africa are still favourites to remain world champions next weekend as they hold a four-point lead over Argentina.
New Zealand's women will also be favoured in Bordeaux. They blew a 26-14 lead over Australia with three minutes to go in the semi-finals.
Australia were pushed into New Zealand's half of the draw after losing to the USA.14-10 in pool play for the first time in eight matches.
But the final was less dramatic. Huge miss-out passes by Australia exposed USA on the wings and Heidi Dennis scored two routine tries in their 22-7 half-time lead.
The 21-year-old Dennis was later named the player of the final thanks to two outstanding try-saving tackles from behind on Alex Sedrick and Sereana Vulaono.
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