Losses to Fiji and Wales had left AustraliaAustralia's campaign on life support and the Wallabies now need Portugal to beat Fiji next week without allowing the Pacific islanders a bonus point.
Richie Arnold, David Porecki and Angus Bell crossed for Australia in the first half and a fourth forward, Fraser McReight, secured the all-important bonus point early in the second half.
Marika Koroibete finally got the Australian backs on the board in the 74th minute but only after the Wallabies had weathered a storm playing with 13 men for the best part of 10 minutes.
"We're still alive. That was the aim of the day," said coach Eddie Jones, who has led Australia to two wins in nine tests this year.
"For a young team down to 13 men we showed plenty of courage and fought hard. We've done that all season, sometimes the results haven't been in our favour... well, most of the time."
Roared on by their own passionate support and most of the neutrals at Stade Geoffrey Guichard, Portugal dominated large parts of the match and were well worth the two tries they scored through Pedro Bettencourt and Rafael Simoes.
If the Portugal that ran the Wallabies ragged for 10 minutes before Bettencourt went over for his 14th minute try turn up against Fiji in Toulouse next Sunday then Australia's campaign might yet have legs.
Unfortunately for Portugal, however, Bettencourt was shown a yellow card for a high hit a minute later and by the time he touched the ball again, Australia had run in three tries.
The Wallabies were still inaccurate at times and Portugal's effervescent running game continued to trouble them as it had their previous pool opponents Wales and Georgia.
Number eight Rob Valetini and prop Bell were a big presence up front, however, and the threat Izaia Perese presented every time he touched the ball in midfield begged the question of why this was his first start of the tournament.
Flanker Nicolas Martins came within an ace of adding a second try for Portugal before being forced into touch and Australia went in at half-time 24-7 ahead but without the bonus point they needed.
McReight resolved that matter when he went over for a try in the 47th minute and gutsy defence repelled the Portuguese from six lineouts close to the line, although replacement hooker Matt Faessler was yellow-carded for collapsing one maul.
Replacement centre Samu Kerevi joined him in the sin bin for a fend to the head of a Portuguese defender but the Australians continued to fight for every yard.
A change of tack to a five-metre scrum finally did the trick for Portugal with replacement lock Rafael Simoes forcing his way over the line to the delight of the majority of the crowd of 41,432.
Koroibete's late try added gloss to the scoreline in what was Australia's second win in nine tests this season but took nothing away from another brilliant performance from the 16th-ranked Portuguese.
