The loss means that Banyana Banyana will not progress out of the group stage of the tournament and will be on the way home after their next match against world champions Japan on Tuesday.
The Canadians first victory means they are lying in third spot ahead of the final games - a point adrift of Japan and Sweden whom they meet on Tuesday at St James' Park. Canada, beaten 2-1 by Japan in their opening match, went ahead after only seven minutes. South Africa lost their first match 4-1 against Sweden.
Melissa Tancredi, who had netted against Japan, was again their marksman when converting a low centre from Diana Matheson. Tancredi was a constant threat and headed just wide at the near post from a Lauren Sesselmann cross while Kaylyn Kyle had a powerful effort saved by Thokozile Mndaweni.
South Africa came more into the game before half-time with Portia Modise's shot on the turn saved by Karina LeBlanc. Then hesitation by Robyn Gayle let in Mpumi Nyandeni only for the Canadian defender to recover and deflect the shot onto the crossbar.
But Sinclair scored her 138th goal for Canada after 58 minutes. Her header from Sesselman's centre hit the underside of the bar but had clearly crossed the line. Canada threatened to add to their lead and a 25 yard drive from Matheson struck the crossbar.
With four minutes left Sinclair broke clear and slid the ball past Mndaweni for her second goal.
It was always going to be tough for the 61st-ranked South Africans, drawn against three of the top seven sides in the world, but it was their defence which let them down badly in the end.
Fifa
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About "the girls" what a stupid name by the way, i saw both of your games. I think our football standard is not there yet. The opponents were very good and too strong for you. All we can say now is try next time.