But thanks to favourable arithmetic, the Swiss will also advance to the final 16 despite the embarrassing outcome of the game against Cameroon, played on artificial turf in Edmonton, Alberta.
Switzerland had taken the lead when Ana Maria Crnogorcevic scored after 24 minutes but goals from Gabrielle Onguene two minutes after the break, and Madeleine Ngono Mani on 62 minutes sealed all three points.
It is only the second time that an African side have made it out of the group stage after Nigeria in 1999.
Cameroon, ranked 53, finish second in Group C with six points behind champions Japan, who beat Ecuador 1-0 on Tuesday, and have a maximum nine points from three games.
As second-placed finishers in Group C Cameroon next play Group A runners-up China in Edmonton on Saturday.
With three points, Switzerland, ranked 19, qualified for the knockout round as one of the four best third-place finishers across the six groups.