The Americans were given a tough test by the Swedes, who drew 3-3 with African champions, Nigeria, in their opener.
Sweden coach Pia Sundhage said her side were finding their momentum after being held in their opener by Nigeria.
“After this match we've gained some confidence,” said former US coach Sundhage. “The opening game was a hard game, I don't think we came up to our level.
“But today it was better, especially dealing with our defending and being tactically smart against one of the best teams in the world,” she said.
Sundhage continued: “If you look back at history Sweden has not played good in the first game and little by little we get better. The fact that we have one of the best goalkeepers in the world is an advantage and she showed that today.”
Australia beat Nigeria in their Group D clash earlier on Friday thanks to two goals from Kyah Simon.
The United States lead the group with four points followed by Australia with three with Sweden on two and Nigeria bottom with one.
In Tuesday's final round of group games in Vancouver's BC Place Stadium, the United States will play Nigeria while Sweden take on Australia in Edmonton – in a game they must win – as they bid for a place in the last 16.