After an afternoon labouring in cold and damp conditions at Moncton on Canada's eastern side, two substitutes began and finished the decisive goal.
Katrina Gorry's fine pass released captain Lisa De Vanna on the right of midfield, and while her shot was fumbled by Brazil keeper Luciana, Simon snuck in to bury the rebound and spark wild celebrations.
She's done it again!! @KyahSimon!! #Bra 0-1 @TheMatildas. WATCH LIVE on SBS http://t.co/CoB4QeF3us #SBSTWG #FIFAWWC http://t.co/2FIux2uWMf — SBS - The World Game (@TheWorldGame) June 21, 2015
It was Australia’s first win over Brazil at a World Cup.
Victory puts the Matildas to the last eight of the tournament for the third straight time, but is the first knockout win for any Australia senior team after the expansion of the FIFA Women's World Cup this year.
► WATCH the moment @TheMatildas created Australian football history, into the #FIFAWWC quarter-finals!! #SBSTWG http://t.co/zElWenlGqj — SBS - The World Game (@TheWorldGame) June 21, 2015
Australia will return to Edmonton for a quarter-final on Sunday morning (AEST), which could be a rematch of the past two Asian Cup finals.
Japan plays Netherlands on Wednesday (AEST) for the right to play Australia, as the Matildas bid to reach the semi-finals for the first time.
Coach Alen Stajcic said it was a deserved result for his team.
"It's a big moment ... it's a massively historic moment," he said.
"Exhilarating is the word for such a victory against a big powerful football nation. The effort, the execution, the spirit has just been brilliant. A lot of sacrifice in the last five months and I guess it pays off on days like this."
Stajcic believes his side can cause problems against any team, given the options he has available to him in attack.
"We're probably one of the most dangerous teams at the World Cup, if not the most dangerous team going forward," he said.
"We've come through three really tough battles and now you can make that four. With such a young team, we've seen so much growth and development in such a short space of time. If they keep growing, we can beat anyone in the world."
A tactical first half in Moncton was devoid of major chances.
Sam Kerr's sweetly connected volley from Emily van Egmond's corner on 10 minutes rippled the side-netting.
Full backs Caitlin Foord and Steph Catley were lively attacking options, although the Matildas had their fair share of ragged moments.
With the half-hour mark looming, Brazil veteran Formiga dispossessed van Egmond, and forced Matildas goalkeeper, Lydia Williams, to make a superb save from her swirling long-range strike.
After the half-time break, the rain came down and the match opened up.
The Matildas had a major life on 63 minutes when the unmarked Formiga headed into the post with the rain teeming down.
De Vanna scurried the ball down the other end, teeing up van Egmond, who shot wide.
Brazil's long-range strikes looked increasingly likely to beat Williams but the keeper held strong.
By 72 minutes, both Gorry and Simon were on the field and, less than 10 minutes later, they made their impact.
After holding out a largely flat Brazilian attack, the Matildas had their slice of history and celebrated wildly on the final whistle.
