The Canadians, skipped by Jennifer Jones of Winnipeg, and the British foursome skipped by Eve Muirhead, waged a tight battle throughout the game.
Canada had scored three in the fifth end to take a 6-3 lead but Britain kept chipping away and pulled to within one in the eighth. Jones restored a two-point lead with a single in the ninth and added an insurance point in the 10th.
Canada also scored a pair in the third and singles in the first and seventh ends.
Muirhead and her British squad (1-2), took doubles in the fourth and sixth ends and singles in the second and eighth.
Canada will play twice on Thursday, against Denmark followed by Switzerland.
In other play, China beat the U.S. 7-4, Sweden downed South Korea 7-4 and Japan doubled Russia 8-4.