Daniil Tarasov made 16 saves on 20 shots for the Blue Jackets (10-21-2), who have lost six in a row. He was replaced by Joonas Korpisalo at 3:24 of the second period, and Korpisalo made 17 saves.
"It's never easy, especially when you get called into the game," said Korpisalo, who sustained a lower-body injury Dec. 9 and missed six games. "It means that things are not going our way. I just tried to make a difference out there."
Kane gave Chicago a 1-0 lead at 13:29 of the first period on a wrist shot from the left face-off circle. It was Kane's first goal since Dec. 3 after going eight games without one.
"It feels good to get a win and feel good about the team's effort, and individual efforts across the board, as well, before we go into break," Kane said. "So, definitely [a] feeling that hopefully we can get more of in the second half of the season.
"It's always nice to produce. I felt like even after the last game (a 4-2 loss against the Nashville Predators on Wednesday), you start feeling good that hopefully things are coming and probably could've had a few more tonight as well."
Domi made it 2-0 at 16:00 on a one-timer after Kane skated in with the puck from the blue line and passed to Domi in the right circle.
Andreas Athanasiou extended Chicago's lead to 3-0 at 2:31 of the second period. Ian Mitchell won the puck along the right-wing boards at center ice and passed to Sam Lafferty, who fed Athanasiou.