Seattle activated Gray on Saturday, when they took a six-game losing streak into their contest against the Indians.
The 29-year-old was claimed on waivers Friday from the Chicago White Sox, where he had a 2.70 ERA in six outings.
Seattle's bullpen is 3-8 with a 4.54 ERA without closer David Aardsma. He had hip surgery in January and recently strained his right elbow during a rehab assignment at Tacoma. Setup man Shawn Kelley had Tommy John surgery in September.
New closer Brandon League started 9 for 9 in save chances, but is 0-4 with three blown saves since last Sunday.
Cortes pitched one scoreless inning for Seattle after being called up April 25.