Matildas edge Brazil to reach quarter-finals
The substitute put away a rebound to secure victory for the Matildas, who had held firm until the only goal of the game in Moncton.
Simon took her tally to three goals for the tournament and it was all Alen Stajcic's team needed.
The win marked Australia's first ever victory in the knockout stages of a World Cup.
Australia will face either Japan or Netherlands in the last eight.
After an even start, Cristiane had the game's first shot on goal in the eighth minute – but Lydia Williams held onto the strike comfortably.
Just three minutes later and the Matildas went close.
Emily van Egmond drifted a corner to the back post and Sam Kerr volleyed powerfully into the side-netting.
Chances were limited in the opening half-hour, with Formiga the next to test Williams – but the goalkeeper tipped her long-range effort over the bar.
Tamires flashed a shot wide for Brazil early in the second half as the rain started to get heavier.
Marta threatened just after the hour-mark as she forced Williams into a low save at her near post.
The biggest chance of the game followed as Formiga headed a corner onto the post.
Williams kept out another long-range Cristiane effort in the 78th minute, but the Matildas went 1-0 up moments later as Brazil conceded for the first time this tournament.
Katrina Gorry played Lisa De Vanna in behind, only for Luciana to save the placed effort.
But Simon was first to the rebound, tapping in the match-winner to see the Matildas through.