Kelly, 25, is still in the rehab process from "Tommy John" elbow reconstruction surgery in the spring of 2015. He opened the season in the Missions bullpen as a way to limit his total innings for the season.
Kelly has a 3.27 earned run average for San Antonio in 22 innings covering 14 appearances.
Kelly's was one of five strong outings by starting pitchers in the Padres minor league system Thursday, although the lack of defense and offense hurt the bottom line.
Triple-A left-hander Jason Lane, 38, allowed five runs on nine hits and a walk over six innings.