This is the eighth major league season for Vargas and all three of his previous shutouts came during the 2011 campaign while he was with Seattle. This is his first season with the Angels, the fourth team for which Vargas has pitched.
Vargas (1-3) had compiled a 5.92 earned run average in his first four starts. He walked two and struck out three against the Orioles.
Mark Trumbo put the Angels in front with a solo homer in the second and the other three Los Angeles runs were driven in by Mike Trout, two of them with a home run in the fifth and another with a single in the seventh.
The first three runs were allowed by starter Miguel Gonzalez (2-2), who surrendered six hits in six innings.