A 52nd minute goal from Josee Belanger earned Canada the victory which sets up a last eight clash with either England or Norway and prompted a post-match celebration heavily tinged with relief.
The Swiss may be World Cup debutants but they matched the hosts in all departments and will head home encouraged by the first outing at this level.
An exit in the round of 16 would have been a huge anti-climax for a Canada team that, inevitably as host nation, have been somewhat over-hyped.
With 53,855 fans packed into BC Place, the weight of expectation hung heavily on the Canadians and at times it showed.
"The pressure has been immense, I’m so proud of the team," said Canada's English coach John Herdman, who was animated on the touchline throughout the game.
The game was played at a frantic pace with neither side able to gain consistent possession or create clear openings.
Switzerland forward Ramona Bachmann was by far the most inventive and dangerous player on the field and she went close to an early opener with a shot to the near post which Canada keeper Erin McLoed got down well to.
The nearest the home side came to breaking the deadlock in a disappointing first half was a looping cross-shot from Belanger which struck the far post and bounced to safety.
The breakthrough came when Rhian Wilkinson crossed from the right and Christine Sinclair smartly laid the ball off to Belanger whose first time shot beat Swiss keeper Gaelle Thalmann.
Bachmann continued to probe the Canada defence but she lacked real support from the Swiss midfield and was too often forced to try and create something alone.
But as they hung on, Canada had McLoed to thank in the 78th minute after she pulled off a great close-range save to foil Vanessa Bernauer.
"We just couldn’t get a goal," Switzerland’s German coach Martina Voss-Tecklenburg.
"The players are disappointed because they allowed just two chances and Canada got that goal and so we are going home."
(Reporting by Simon Evans in Edmonton, editing by Nick Mulvenney)
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