Brazil kept alive their pursuit of an historic first Women's World Cup title as they edged an entertaining quarter-final clash with Australia.

The Brazilians looked to have had the game wrapped up when they stormed into a two-goal lead with less than 30 minutes gone through Formiga and Marta.

But Australia pulled one back in the 36th minute through Lisa De Vanna, the first time the Brazil defence had been breached in the tournament, before they restored parity in the 68th minute through Lauren Colthorpe.

But Cristiane grabbed the winner for Brazil with 15 minutes left.

The victory means Brazil will meet the United States in the semi-finals.

Brazil had made the ideal start in the fourth minute as Formiga struck the ball from the edge of the box over the head of goalkeeper Melissa Barbieri and off the underside of the crossbar into the back of the net.

Australia were dealt a further blow in the 20th minute when influential captain Cheryl Salisbury, who had scored the equaliser against Canada to book their place in the quarter-finals, had to go off due to injury.

And things got worse when Brazil doubled their advantage three minutes later.

Renata Costa was fouled just inside the area and Marta stepped up to successfully convert the resulting penalty.

Australia pulled a goal back nine minutes before the break when a defensive error presented the ball to De Vanna and the forward skipped past goalkeeper Andreia before sliding the ball into the empty net.

The South Americans came out strong in the second period but were finding chances limited against a well-organised Australia defence.

And Tom Sermanni's side equalised with a superb goal in the 68th minute when, from a free-kick, Colthorpe glanced a header over the despairing arms of Andreia and into the back of the net.

But Brazil restored their lead just seven minutes later with a crisp strike from Cristiane when, with her back to goal, the Wolfsburg striker collected the ball before making a sharp turn and launching an unstoppable shot into the back of the net.

Cristiane could have had another goal seconds later but she mis-controlled the ball when she would have been clear on goal.

Australia volleyed over in injury time before Daniela's goalbound effort was headed behind by Dianne Alagich.

Seconds later the final whistle was blown to confirm Brazil's place among the final four.