Australia players celebrate after winning against France. Reuters

Co-hosts Australia beat France 7-6 in a thrilling penalty shoot-out to reach the semi-finals of the Women's World Cup for the first time in their history on a night of drama in Brisbane on Saturday.

Australia now go to Sydney on Wednesday to face England in the semi-final.

Cortnee Vine scored the winning penalty to end a remarkable shoot-out that saw both teams take 10 spot-kicks, the quarter-final having ended 0-0 after 120 nerve-shredding minutes.

Vine held her nerve to send the crowd into raptures and keep the Matildas' dream of winning the World Cup on home soil alive.

Australia goalkeeper Mackenzie Arnold missed a chance to win the shoot-out when her kick hit the post, but then saved twice from Kenza Dali after the VAR spotted she had both feet off her line the first time.

Vicki Becho missed France's 10th penalty, and it was left to Vine to take Australia through by beating France's substitute goalkeeper Solene Durand, who had been sent on especially for the shoot-out.

Australia's players celebrate their victory after a penalty shoot-out in Brisbane on Saturday. AFP

It was an agonising way for France to go out after a tense encounter watched by a sell-out crowd of 49,461.

Les Bleues had been hoping to get to the semi-finals for just the second time, following their defeat in the last four in 2011, but instead go home.

Australia's victory was achieved despite Sam Kerr again being left on the bench at kick-off, with the talismanic Matildas captain, now fit after a calf injury, coming on early in the second half and going on to convert her penalty in the shoot-out.

Agence France-Presse