Kopech struck out 10 in five innings as the Sox beat the Rangers 8-4 to sweep the three-game series. He allowed one run on four hits on 87 pitches.
Kopech has primarily been used out of the bullpen this season. He was a spot starter for Game 2 of a doubleheader against the Boston Red Sox on April 18 at Fenway Park; it was his first start since Sept. 5, 2018.
Lucas Giolito was originally scheduled to start Sunday, but he said he cut the top of the middle finger on his pitching hand while the team was in Cleveland on Monday night.