Marta's 16th Women's World Cup goal was not enough to inspire Brazil to victory as Australia rallied to a controversial 3-2 win Thursday in Group C. 

Brazil's record scorer, who went off injured at halftime, moved level with Miroslav Klose's tally of goals at World Cup finals when she opened the scoring in Montpellier with a 27th-minute penalty.

Cristiane followed up on her hat trick from the opening win over Jamaica to add a second, but Caitlin Foord gave Australia hope.

And after Chloe Logarzo's fortuitous strike had restored parity, Australia completed a famous comeback when Monica headed into her own net and Sam Kerr was deemed not to be interfering in a contentious decision.

Australia wanted a penalty in the 20th minute when Thaisa bundled into Tameka Yallop, but referee Esther Staubli waved away their appeals and the decision stood after VAR adjudged the Matildas midfielder handled in the build-up.

Matters were made worse for Australia when Elise Kellond-Knight recklessly dragged down Leticia Santos and Marta sent Lydia Williams the wrong way from the resultant spot-kick, becoming the first player to score at five Women's World Cups in the process.

Brazil's other leading star Cristiane was on hand to double the advantage seven minutes before halftime, towering above her marker to head Debinha's cross home.

Australia rallied and after Kerr had failed to turn in from close range, Foord made no such mistake with an instinctive finish from Logarzo's flick-on.

Having conceded its first World Cup group-stage goal since the 2003 tournament, Brazil was dealt another blow following the restart, with Marta, who missed the opening game due to a thigh injury, unable to continue.

Australia picked up where it left off and equalized when Logarzo's long-range effort found its way through a crowd of players.

Brazil's misery was compounded eight minutes later. Monica inadvertently turned Emily van Egmond's ball beyond Barbara, and although an offside call against Kerr seemed to have bailed out the Brazilians, the decision was overturned after a VAR review and Vadao's side slumped to a humiliating defeat.