After a bright start from the Matildas, VAR was required to rule on a possible penalty for the green and gold in the 20th minute only for a handball earlier in the play to deny Australia a spot-kick.
Brazil would then go up the other end and win a penalty of their own with VAR ruling Elise Kellond-Knight was guilty of shirt pulling inside the box.
Veteran Brazilian striker Marta made no mistake from the spot to score in a fifth World Cup and hand her side the lead in the 27th minute.
Just over 10 minutes later, Cristiane would double Brazil's lead with a thumping header following a slick team move.
Staring down the barrel of costly consecutive World Cup defeats, Australia pulled a goal back in first-half injury-time as Caitlin Foord converted from close range after a cross was kept alive by Chloe Logarzo.
With the momentum in the second 45 minutes, the Matildas would draw level in the 58th minute with Logarzo's long-range effort somehow bouncing between Brazil's defenders and keeper and into the back of the net.
Australia's incredible turnaround would then be completed in the 67th minute via an own goal as Brazilian defender Monica headed the ball into her own net.
Though the goal was initially ruled out for an offside call on Sam Kerr, the Matildas captain was deemed to have not interfered with play on VAR review as the green and gold took the lead for the first time.
Australia would not surrender it in the final minutes either as they claimed a vital 3-2 win over Brazil - the Matildas fifth straight win against the South Americans and Brazil's first group stage loss at a World Cup since 1995.
The green and gold will now round out the group stage against Jamaica with progress to the Round of 16 now firmly in their own hands.