Sinclair, who is reportedly appearing at her 290th international tournament, has now reached 185 goals in her international career, breaking a record previously held by American player Abby Wambach.
Sinclair scored her historic goal in the 23rd minute of the game, after tying her record with a penalty in the seventh minute.
In addition to Saint Kitts and Nevis, Canada's group for Olympic qualifying includes Jamaica and Mexico.
If Canada bests te group, it will play then in the semifinals in Carson, California, on 7 February. The opposite group, which includes the United States, Costa Rica, Haiti and Panama, is playing matches in Houston.
The top two seeds in the tournament will qualify for the Olympics in Tokyo this summer.