Australia battled back from 2-0 down to win an extraordinary game after Brazil legend Marta had earlier scored a record 16th Women's World Cup goal.
The six-time world player of the year, 33, opened the scoring from the penalty spot, before 34-year-old striker Cristiane brilliantly headed in her fourth goal in two games to double the lead.
But the Matildas levelled through Caitlin Foord's poked finish and Chloe Logarzo's cross-shot either side of half-time, with Marta having to be withdrawn with a knock during the break.
And defender Monica's unfortunate own goal - which was eventually awarded by VAR, with an offside Sam Kerr controversially judged not to have been interfering - completed Australia's remarkable comeback.
The Matildas, who are ranked sixth in the world but suffered a surprise loss to Italy in their opening game on Sunday, are now level with Brazil and the Italians on three points in Group C.
Jamaica and Italy meet in their second match in Reims on Friday, in the most evenly-poised group of the tournament.