The Canadian women have won a medal in each of the four Olympics in which curling has been contested, but their only gold came in the debut year of the sport in 1998.
Canada took a 6-3 lead through five ends against the British team, but was ahead by only a point heading into the ninth.
The victory boosted Canada to 3-0, the same record posted by Switzerland. The Swiss had the day off Wednesday.
China, Japan and Sweden shared third place at 2-1 with all of those countries winning on Wednesday.
China downed the United States 7-4 to keep the Americans winless in four matches, Japan got past Russia 8-4 and two-time defending champion Sweden was a 7-4 winner over South Korea.
A nine-match round-robin tournament will be held in Sochi with the top four countries then moving on to the semifinals.
Switzerland and Canada will meet late Thursday in what will be the second match of the day for both sides. The Swiss will have an early meeting with Sweden and Canada will take on Denmark.