Britain has now lost both games in its first Olympics since 1948.
Courtnay Pilypaitis and Kim Smith added 11 points each for Canada (1-1), which closed out strong after blowing a 10-point lead late in its opening loss to Russia.
"I felt a lot of things weren't going our way, it wasn't pretty basketball, but we pulled out the win and that’s what's important," Thorburn said.
Natalie Stafford and Johannah Leedham had 15 points each for Britain, which led 61-57 late in the fourth quarter.
But Thorburn drove to the basket to tie at 61-61 with four minutes left as Canada finished the game on a 16-4 run. Thorburn hit a three-pointer to the burst to put Canada ahead 66-61. She also scored the last three points of the game, all free throws.
Canada got off to a good start defensively in the game, forcing seven turnovers in the first quarter. Thorburn hit a three-pointer at the buzzer to give Canada a 19-15 lead after the first frame.
Canada went into the half with a 36-32 lead after a back-and-forth second quarter.
After a sloppy third quarter from both teams, Britain went on an early run to take the 61-57 lead with 6:10 left in the game.
Unlike the loss to Russia, Canada was able to battle back and dig themselves out with a late run.