Trailing 2-0 and with their qualification hopes appearing dead, Caitlin Foord and Chloe Logarzo brought Australia back from the brink before Monica's own goal gifted the Matildas a priceless win.

It is only the second time a team have come from 2-0 down to win at the Women's World Cup.

After a first-up loss to Italy and early goals by Brazilian duo Marta and Cristiane, the Matildas were on the rack in Montpellier.

Instead of collapsing, the grit and verve synonymous with the side came to the fore.

Within the confines of the 90 minutes, this was a fantastic win.

But given the weight of expectations and negativity in the air, it was an all-time classic.

"Tonight, this was one of the finest Australian performances I've seen," coach Ante Milicic said.

Weighty praise given the 45-year-old's long-standing involvement in Australian national teams.

Captain Sam Kerr revealed the weight of pressure on the team with her first comments after the match.

"There were a lot of critics talking about us but we're back. So suck on that," she said. "We don't listen to the haters.

Look at that performance to come back from the deep. You can see what it means to us.

"We were so disappointed after the first game. Brazil are a top-10 team so the reaction from the girls at half time, I love these girls.

"And we're back in it."

In 90 emotion-charged minutes at the Stade de la Mosson, Australia turned the wheel on their potential car crash campaign to have control of their destiny.

They will seal qualification for the next phase by defeating Jamaica on Wednesday (AEST), and can hope again of a deep run in France.

Against Brazil, Logarzo's power of running was immense, Tameka Yallop was relentless and Kerr made her infrequent contributions tell.

There was also controversy, particularly with their winner.

Kerr was plainly in an offside position when Emily van Egmond played a long ball but the referee saw her - with the help of the video assistant - as not interfering with play while defender Monica headed the ball past goalkeeper Barbara.

The first goal was also contentious.

On 27 minutes, Brazil raced forward and won a penalty when Elise Kellond-Knight faintly grabbed Leticia Santos' shirt in the box.

Marta converted from the penalty spot for a record-breaking strike.

With her 16th World Cup goal, the Brazilian legend became the first woman to score at five tournaments.

Further pain was to come 10 minutes later, when Cristiane doubled the South Americans' lead.

Tamires nutmegged Emily Gielnik and released Debinha, who laid an inviting cross for Cristiane to rise above a flat-footed Steph Catley and nod past Lydia Williams.

Humiliated, arguing amongst themselves, and two down, the Matildas set off on a rescue mission and two of Australia's hardest workers put the Matildas on the board.

Yallop fired in a cross to find her midfield partner Logarzo, who headed across goal for Foord to bundle home.

The strike, in first-half injury time, gave the Matildas confidence as they headed into the break.

Their fire was evident from the get-go, and soon enough the game was back on terms.

On 58 minutes, Logarzo fizzed the ball across goal and Barbara, distracted by the run of Kerr, lost track of the shot and let it in at her back post.

Australia were level, and with all the momentum, pushed on for a record-breaking win, becoming the first team has to come from behind to defeat Brazil at the Women's World Cup.

The only other side to come back from a two-goal deficit against any opponent was Sweden against Germany in 1995.