In front of a crowd of nearly 50,000, Sweden took the lead with a 30th-minute penalty by Fridolina Rolfo and doubled their advantage with a powerful strike from Kosovare Asllani just after the hour.
Ranked third in the world, this is the fourth time that Sweden have finished third at the tournament.
They fully deserved their win against the hosts, dominating the midfield and keeping talismanic Australian striker Sam Kerr relatively quiet.
Australia's other dangerous attacker, Mary Fowler, had a night to forget as she struggled physically against the size and power of the Swedish defenders.
By contrast, Sweden striker Stina Blackstenius caused havoc among the Australian defence during her 63 minutes on the pitch and had a hand in both goals.
The Swedes opened the match with far more intent than the Matildas and dominated for most of the first period.
Playing a bit like England in their 3-1 semi-final win over the Matildas on Wednesday, the Swedes slowed the ball down and controlled the midfield.
Australia only really looked dangerous on the transition and for much of the time they seemed to be chasing shadows, struggling to get any meaningful possession.
The Swedes had a golden chance to take the lead in the first 60 seconds when Blackstenius shot low across goal.
Australian goalkeeper Mackenzie Arnold, who had another excellent night, parried the ball away and Ellie Carpenter did well to clear from in front of an open goal.
The Matildas didn't have their first shot until the 24th minute when a Hayley Raso drive drew a good save from Sweden keeper Zecira Musovic.
But minutes later Sweden took the lead when VAR ruled that Clare Hunt had clipped Blackstenius's heel after yet another dangerous run into the box from the Swedish striker.
Australian coach Tony Gustavsson made an attacking change on the 60-minute mark, bringing on Emily van Egmond and Cortnee Vine, but it was Sweden who continued to control the match.
They went some way to silencing the sell-out crowd when Blackstenius laid a ball across goal for Asllani, who smashed a powerful strike past a diving Arnold.
It was their last contribution of the night as both were subbed almost immediately.
Australia tried desperately to breach the Swedish defense in the last 20 minutes with deep crosses into the box but Musovic was largely untroubled to keep a clean sheet.