Lina Hurtig put Sweden ahead off a set piece in the 38th minute before Megan Rapinoe's penalty kick pulled the United States even in the 87th. The draw extended the U.S. team's unbeaten streak to 38 games.
Rapinoe's goal was her sixth this year to lead the team.
The United States travels to Le Havre for a match against No. 3 France on Tuesday.
The Americans have not lost a match since January 2019, when they fell to France. Their 16-game winning streak was the third longest in team history. Lloyd wore the captain's armband for her milestone game.
The only other players to appear in 300 or more games for the national team are Kristine Lilly (354) and Christie Pearce Rampone (311). The Swedes shocked the Americans in the quarterfinals of the 2016 Olympics, advancing on penalties after a 1-1 draw.
Depsite the draw, U.S. manager Vlatko Andonovski saw some positive from the result.
"I wouldn't say one of the best things that happened to us, but something that is very good for us," he said. "In fact, that's why we came here. We came here to play good teams. We came [to] Europe to play opponents, to some extent get exposed to different tactics, high level tactics, organized teams and to try to overcome all that."
Sweden went on to play in the final in Rio de Janeiro but fell to Germany. Both teams have qualified for the Tokyo Olympics this summer. The United States is the top-ranked team in the world.
In Tokyo, the Americans will seek to become the first women's team to follow a World Cup victory with an Olympic gold medal.
The Olympics will present more difficult challenges, Rapinoe said, and the United States must get better at adapting.
"It's going to be games where physically we're not at our best because we've just played, or it's really hot, or a team switches up tactics, or we're just not playing well that day," Rapinoe explained. "So I think individually, but really sort of collectively, we need to be able to understand what's happening in the moment very quickly and adjust. We can't just play one way all the time.''