Switzerland, ranked No. 19 in the world, falls to 1-1-0 in Group B with the loss. The United States, sitting atop the group, plays Iceland in the final group match on Monday.
The Americans have won the Algarve Cup nine times in the tournament's 22-year history. The 12-team field this year includes nine teams that will play in the Women's World Cup starting in June.
The United States won the tournament opener 2-1 over Norway on Wednesday.
Solo was suspended in January following the arrest of her husband, former Seattle Seahawks tight end Jerramy Stevens, for driving under the influence in a U.S. Soccer van. Solo, who was in training camp in Southern California at the time, was also in the van.
The United States improves to 3-1-0 this year. The United States opened 2015 with a pair of exhibitions, a 2-0 loss to France and a 1-0 victory over England.
U.S. coach Jill Ellis continued to tinker with her lineup in the match as the team prepares for the World Cup. The United States opens Group D play with Australia in Winnipeg, Manitoba, on June 8.