It was a disastrous opening to the match for the Matildas who conceded after only 20 seconds when Canada's Janine Beckie netted. Beckie's goal was the fastest in Olympic Gamess history.
The Matildas were given a lifeline in the 18th minute when Shelina Zadorsky was given a straight red card for pulling Michelle Heyman down when the Australia striker went up for a header.
With an extra player advantage Australia took control of the first half but were unable to find the back of the net.
Canada returned galvanized in the second half and had a chance to double their lead in 72nd minute when the referee awarded them a penalty after a Claire Polkinghorne handball.
However, Matildas shot stopper Lydia Williams was up to the task and denied a lame penalty from Beckie.
Williams's save should have been another turning point for Australia but it was Canada on the up.
Any hope of a Matildas comeback was killed off in the 80th minute when Christie Sinclair doubled Canada's lead when she beat a stranded Williams with a well-placed shot from distance.
Australia next play Sunday (AEST) when they take on world number two side Germany in their second match of the tournament.
Olympic Games Women's Results
Group E
Sweden 1 - 0 South Africa
Brazil 3 - 0 China
Group F
Canada 2-0 AUSTRALIA
Zimbabwe 1-6 Germany
Group G
United States 2 - 0 New Zealand
France 4-0 Colombia
