In the 2018–19 season, on January 14, 2019, Cogliano was traded by the Ducks to the Dallas Stars in exchange for Devin Shore. On February 26, 2019, while playing against the Vegas Golden Knights, Cogliano left the game with an upper body injury after being hit by Ryan Reaves. He sat out the next game on February 28 against the Los Angeles Kings. It was his first game missed in his NHL career for a reason other than a suspension. He missed the next two games after that, and a fourth in April that season.