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.
Instead of collapsing, the grit and verve synonymous with the side came to the fore.
Within the confines of the 90 minutes, this was a fantastic win.
Given the weight of expectations and negativity in the air, it was an all-time classic.
Logarzo's power of running was immense, Tameka Yallop was relentless and Sam Kerr made her infrequent contributions tell.
But against the run of play, Australia found themselves behind on 27 minutes.
Elise Kellond-Knight grabbed Leticia Santos' shirt in the box and Marta converted from the penalty spot for a record-breaking strike.
With her 16th World Cup goal, the Brazilian legend became the first woman to score at five tournaments.
Further pain was to come 10 minutes later, when Cristiane doubled the South Americans' lead.
Tamires nutmegged Emily Gielnik and released Debinha, whose inviting cross was met by Cristiane, who rose above a flat-footed Steph Catley to nod past Lydia Williams.
Humiliated, arguing amongst themselves, and two down, the Matildas set off on a rescue mission.
Kerr was seeing more of the ball and Gielnik had a sighter, but it was two of Australia's hardest workers that put the Matildas on the board.
Yallop fired in a cross to find her midfield partner Logarzo, who headed down for Foord to bundle home and punish some woeful Brazilian defending.
The strike, in first-half injury time, gave the Matildas a modicum of confidence as they headed into the break.
Their fire was evident from the get-go, and soon enough the game was back on level terms.
On 58 minutes, Logarzo fizzed the ball across goal and Barbara, distracted by the run of Kerr, somehow lost track of the shot and let it in at her back post.
Australia were level and, with all the momentum, pushed on.
Kerr was again involved for Australia's winner, keeping the defence busy as Emily van Egmond's long ball was unfortunately headed home by Monica.
The 66th-minute strike was subject to a long VAR discussion, with Brazil claiming Kerr was in an offside position when Monica's flicked header sailed past Barbara and into the net.
However, the goal stood and the Matildas held on comfortably for the last 25 minutes to seal a crucial win.
Source AAP
