Brandon McCarthy went on the 15-day disabled list because of a stress fracture in his right shoulder blade, and Kris Benson was sent outright to Oklahoma City.
Grilli, a right-hander, is 0-1 with a 6.05 earned run average and one save in his eighth major league season. His 16-16 with a 4.74 ERA and two saves in his career. The Rockies had designated Grilli for assignment Friday.
Moscoso was 4-1 with a 4.10 ERA in 10 games, including eight starts, between Double-A Frisco and Oklahoma City.
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Benson returned to the majors this season after a two-year absence. He was 1-1 with an 8.46 ERA in eight games, including two starts.