Trailing 2-0 and with their qualification hopes appearing dead, Caitlin Foord and Chloe Logarzo brought Australia back from the mire, before Monica's own goal gifted the Matildas a priceless win.
It is only the second time a team have come from 2-0 down to win at the Women's World Cup, with Sweden, who beat Germany in 1995, the only other side to muster a similar comeback.
After a first-up loss to Italy and early goals by Brazilian duo Marta and Cristiane, the Matildas were on the rack in Montpellier.
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