Roslovic made it 3-1 at 14:21 when he got to a loose puck in the slot. He has scored 12 goals this season, matching his NHL career high from the past two seasons.
Sean Kuraly scored into an empty net at 18:23 of the third period for the 4-1 final.
"You've got to learn how to play with a lead," Columbus coach Brad Larsen said. "In the third period there, they're going to make their push, they're going to get some chances, but I thought we did a good job of minimizing the Grade-A chances, doing a good job in front of Elvis. And he made some saves at key times for us."
Chabot left the game midway through the second period with an upper-body injury. The defenseman was hit by Kuraly and was favoring his right hand for a few shifts afterward.
"I think, for us, we're still a young team, but we're getting to a point where when we're up in games we can't be turning pucks over," Senators forward Colin White said. "We've got to put it deep. I think we're still a pretty positive team, but the goals aren't coming, and it gets frustrating. I think we just need to keep coming to the rink and working hard and stick together to get through it."
NOTES: Smith said Chabot "looks like he's going to be out a while." … Senators forward Chris Tierney had an assist in 11:07 after missing eight games with a lower-body injury. … Blue Jackets forward Jakub Voracek had one shot in 14:47 after missing one game with a knee injury. On Friday, Voracek collided with Minnesota Wild forward Marcus Foligno, who was fined $5,000 for the hit. … The Blue Jackets lead the NHL with 21 comeback wins this season, the most in their history (20, 2018-19, 2005-06). … Columbus plays the Washington Capitals on Thursday.