The Scottish skip, a silver medallist three years ago, opened strongly alongside her rink of Anna Sloan, Vicki Adams and Claire Hamilton.
But Canada's Rachel Homan quickly responded, with the game close until Scotland scored in the eighth and ninth ends for a 6-4 win.
"It was one of our goals when we came out here - to get off to a good start, and especially against Canada," said Muirhead.
"We know Canada is such a good team and it's always close games against them.
"We got off to a great start and then unfortunately for them they had the fall in the second end which gave us a steal of one."
Scotland will continue their campaign in Riga with group matches against unbeaten rivals Sweden and Germany on Sunday.