The Matildas have mounted a stunning comeback from 2-0 down in the first half, emerging victorious with a 3-2 win over familiar foes Brazil at the Women's World Cup in Montpellier, France.

Brazil took an early lead with a penalty awarded off a rough defensive tackle by Elise Kellond-Knight.

It was a controversial call, especially as Tamika Yallop had gone down in the box after a foul by Thaisa minutes before, but it was voided due to a handball in the build-up.

Central defender Alanna Kennedy was adamant there had been a handball before this foul, too, but the VAR disagreed.

Superstar Marta stepped up and buried the ball past goalkeeper Lydia Williams with ease.

The first deadly attack from open play came from a nutmeg by Tamires through the legs of Emily Gielnik, finding Debinha with plenty of space down the left flank.

A cross from her reached Cristiane in front of the goal mouth, who defied Stephanie Cately's defence to head it home.

At this point, the scoreboard did not accurately reflect the competitiveness between the two sides.

As predicted, the game was all about the attackers. No sooner had the Brazilians given Williams a scare, the Matildas were giving Brazilian goalkeeper Barbara the same treatment.

The comeback began soon after as the Matildas launched wave after wave of attack.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 29 seconds 29 s Matildas captain Sam Kerr after win over Brazil (Photo: Reuters)

It paid off right before half-time as a messy scuffle in front of the goal saw Caitlin Foord slide the ball past the keeper.

On the climb, the Matildas kept up the pressure into the second half.

A long ball from Chloe Logarzo meant for Sam Kerr passed just out of her reach, and Barbara's, to equalise for Australia.

The final goal came after a nail-biting VAR check.

An own goal by Monica was questioned after Kerr had come from offside to pressure the ball alongside Sousa.

But, without a touch from Kerr officially interfering with Monica, the offside was deemed inconsequential and the goal was counted.

Captain Kerr was all smiles when the full-time whistle was blown, telling her team's critics to "suck on that one".

Australia is only the second team in Women's World Cup history to win a match from being at least two goals behind, after Sweden beat Germany 3-2 in 1995.

Brazil and Australia have three points each in Group C, as do Italy, who take on Jamaica tonight after beating the Matildas in their opening match.

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

"The players deserve all the rewards they were given tonight. I'm really delighted for them.

"They never stopped believing, and the coaching staff never stopped believing.

"We kept on believing in our style and in our football and it's an Australian performance to be proud of."

Brazil's Marta, right, battles for the ball with Australia's Ellie Carpenter in Montpellier. ( AP: Claude Paris )

See how the match unfolded in our live blog.