Australia didn't hesitate in showing their intent as Megan Schutt struck early with her third ball, handing Mooney with an easy catch at point to remove Hasini Perera for a duck.
After the powerplay, Umesha Thimeshani was removed by Carey for 20.
It was yet another impressive outing for Athapaththu against the Australians, her 38-ball half-century taking Sri Lanka to 91 but the hosts finally took their third wicket when the captain blasted the ball straight to her opposite number Lanning.
Anushka Sanjeewani's 25 helped Sri Lanka inch to three figures but she was soon caught by Delissa Kimmince off Strano's bowling, while Ama Kanchana perished for a duck two balls later.
Two boundaries from Nilakshi de Silva in her late cameo helped Sri Lanka get to 120 but she was stumped by Healy in Jonassen's final over.
Australia witnessed a horrible start to their chase with Udeshika Prabodani bowling Healy for a duck in the second ball.
And Prabodani's second over started just as brightly as her first as she produced another stunning in-swing delivery to remove Gardner for two.
The hosts, who knew the importance of a win at the WACA after losing to India in Sydney, soon found themselves in deep trouble when Sanjeewani stumped Mooney to leave them tottering at 10 for three after 20 balls.
But Haynes came to Australia's rescue and in the company Lanning took Australia home.
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