Schmidt, making her 100th national team appearance, scored in the game's second minute. Matheson, who scored to lift Canada over France for bronze at last summer's London Olympics, gave the No. 7-ranked Canadians a two-goal lead in the 79th minute, chipping the ball over the Swiss goalkeeper.
"I'm just so proud to have represented Canada for these 100 caps. Proud of the effort the team put in today," said Schmidt, who wore the captain's armband for the game.
Switzerland is ranked 26th in the world.
"It was good to get a win in our opening match of the tournament," said head coach John Herdman after the game.
"We scored early which gave us the advantage , but the Swiss did well during spells of the match so we know we have some things to improve on as well."
The Canadians will have star striker Christine Sinclair back in the lineup for Friday's game against No. 19 Finland. Wednesday marked the final match of Sinclair's four-game suspension, which she received for an incident following Canada's overtime loss to the United States at the London Games.
Canada caps the preliminary round with a game against the Netherlands (No. 14) on Monday.