A Fridolina Rolfo penalty and sweetly-struck Kosovare Asllani effort either side of the half time whistle saw the Blue and Yellow finish third for the second tournament running, while they also nabbed the final spot on the podium in 1991 and 2011.
A fourth-placed standing represents Australia's best-ever finish at a Women's World Cup, but it was a bitterly disappointing end for Tony Gustavsson's side, whose star striker Sam Kerr was little more than a spectator over the 90 minutes.
Making a fast start to the game that no team wants to play, Sweden exploded out of the blocks against the co-hosts, whose number one Mackenzie Arnold had to beat away a Stina Blackstenius drive with just two minutes on the clock.
The Blue and Yellow maintained their intensity for the opening 15 minutes before Australia began to settle, as Hayley Raso stung the palms of Zecira Musovic with a top-corner bound strike in the 22nd minute.
The Matildas thought they had escaped a heart-in-mouth moment when Rolfo's 28th-minute header rattled the woodwork, but play was brought back for a foul on Blackstenius by Clare Hunt in the build-up, and Sweden were awarded a spot kick following a VAR review.
Rolfo stepped up to the 12-yard mark and succeeded with a low penalty down to Arnold's left - the Australia shot-stopper went the right way but was beaten by the pinpoint accuracy of the 29-year-old's penalty.
Sweden looked the more likely to score again as the first half entered its dying embers, and Arnold had to be alert in injury time to parry a close-range Filippa Angeldahl effort after her defenders made a mess of Asllani's free kick.
A nasty clash of heads between Asllani and Caitlin Foord brought an end to a first half in which frustrations were starting to boil over, although both players were given the green light to return for the second half, Foord having been patched up.
In contrast, Asllani showed few ill effects from that collision and deservedly doubled Sweden's tally in the 62nd minute, releasing Blackstenius down the left and receiving the ball back from the Arsenal attacker before unleashing a crisp 20-yard strike into the bottom corner.
Australia were agonisingly close to halving the deficit eight minutes later, but Clare Polkinghorne's toe-poke from close range was straight at Musovic, and the Matildas' subsequent attempts to give the Brisbane crowd something to cheer were futile.
Sweden's success precedes Sunday's highly-anticipated showpiece match between first-time finalists England and Spain, which kicks off at 11am UK time at Stadium Australia in Sydney.