Brazil won the shoot-out by 7-6 after 120 minutes of play in ordinary and extra time.
Australia's Matildas and the host nation were all square at 4-4 when five-time world player of the year Marta stepped up to the spot.
But goalkeeper Lydia Williams made an excellent save, giving Katrina Gorry a golden opportunity to slot the game-winner.
Again it was the goalkeeper who stood tallest, with Barbara diving to her right to make a brilliant save to deny the 2014 AFC women's player of the year.
Brazil's Debinha and Monica, and Aussies Michelle Heyman and Chloe Logarzo netted next, before Tamires nailed what turned out to be the decisive goal into the top-right corner.
The pressure was then on Alanna Kennedy to step up to the plate, but she could not send her strike past the outstretched left glove of Barbara.
Coach Alen Stajcic said Kennedy was not to blame for missing her spot kick at the shootout.
"Better players than her have missed penalties. I've seen Maradona and Messi and everyone miss penalties," he said.
"That happens in a shoot-out. Marta missed as well, so that's what happens in a shoot-out."
Forward Caitlin Foord tweeted after the game that she was "shattered".
"Proud of everyone tonight, we gave it everything. Thanks for all the support," she said.
Co-captain Clare Polkinghorne tweeted: "No words. Just proud and honoured to stand beside these amazing footballers."
Brazil will play Sweden, who knocked out defending Olympic and world champions USA, in the last four.
Canada and Germany will play out the other semi-final.
The Canadians maintained their perfect record in Brazil thanks to Sophie Schmidt's winner in a 1-0 victory over France.
Meanwhile, Germany overcame 10-woman China in Salvador with Melanie Behringer scoring the game-winning foal 14 minutes from the end of the match.