It was Canada who started the match the better, with Kaylyn Kyle causing problems down the South African right side, but all too often her final ball was lacking.
Canada did take the lead, however, after just seven minutes when Melissa Tancredi tapped home from close range.
Canada continued to push for the second late in the half with Kyle coming close, while the South African threat came from the direct running of Portia Modise.
For all Canada's dominance, they could have been level when Mpumi Nyandeni latched onto a defensive mix-up late in the half, but she could only find the crossbar from close range.
It was South Africa who started the second period the better, and Andisiwe Mgoyi missed a wonderful chance with 55 minutes on the clock.
They continued to play the better football as the match advanced, but Sinclair tested the palms of Mndaweni before eventually scoring her side's second with a tap-in just before the hour mark.
Sinclair added her second of the game in the latter stages to secure goal number 140 for her country - and all the points.