Ramona Bachmann, who had several quality runs on goal in the second half for Switzerland, had an open shot in the box in the final minute of stoppage time -- pushing the ball just over the goal.
Japan plays Cameroon on Friday, while Switzerland faces Ecuador.
Nigeria 3, Sweden 3: Francisca Ordega's 87th-minute goal pulled Nigeria into a tie with Sweden in Winnipeg, Manitoba.
Linda Sembrant came off the bench to put Sweden ahead 3-2 before Ordega's drive sailed between goalkeeper Hedvig Lindahl's legs.
While Ordega celebrated with her teammates, Nigeria coach Edwin Okon dropped to his knees and kissed the turf on the sidelines.
Nilla Fischer put Sweden up 2-0 in the first half with a goal in the 31st minute after Nigeria conceded an own goal. Nigeria evened it in the second half when Ngozi Okobi and Asisat Oshoala scored in a three-minute span.
It was the tournament opener for both teams, who are in Group D along with the United States and Australia. An expanded field of 24 teams is playing in the monthlong World Cup. Fifth-ranked Sweden, under former U.S. coach Pia Sundhage, faces her former team Friday in one of the most anticipated matches of the group stage.
Cameroon 6, Ecuador 0: Cameroon scored three goals in a nine-minute stretch late in the first half and routed Ecuador in Vancouver in the Women's World Cup debuts for both nations.
Gaelle Enganamouit had a hat trick for 53rd-ranked Cameroon, which converted three penalty kicks. Enganamouit scored in the 36th and 73rd minutes, then got a penalty kick in the fourth minute of stoppage time.
Madeleine Ngono Mani put Les Lionnes ahead in the 34th minute, and captain Christine Manie's penalty kick made it 3-0 in the 44th.
Aboudi Onguene converted a penalty kick in the 79th,
Ligia Moreira of 48th-ranked Ecuador was given a red card for a foul in the 66th minute.
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