Kane sent a backhand pass to the slot for Pius Suter, who extended the lead to 3-1 at 13:30 with a tap-in goal.
Roslovic's one-timer on the power play from the top of the right face-off circle made it 3-2 with 2:00 remaining. Chicago had been 12-for-12 on the penalty kill in its previous five games.
Kane made it 4-2 29 seconds into the third period with a power-play goal from the right circle.
Boone Jenner and Roslovic scored 1:20 apart to tie it 4-4. Jenner made it 4-3 at 6:39 when he knocked in a loose puck from Atkinson's shot in front of the net, then Roslovic scored his second with a shot from the right circle to tie it 4-4 at 7:59.
"We made some plays, some guys made some plays," Blue Jackets coach John Tortorella said. "You could just see some confidence grow. I thought we still had some breakdowns and still gave up some chances, but I just liked the way we made some plays. We made some passes and we climbed out of corners in the offensive zone. Our [defensemen] were involved in motion offensively, so that's a good sign."
DeBrincat made it 5-4 at 13:05 with a one-timer from the left face-off circle off a Kane backhand pass.
Michael Del Zotto scored his first goal with the Blue Jackets to tie it 5-5 with 2:41 remaining with a shot from the left circle. He had an assist on Stenlund's game-winner. The defenseman signed a one-year contract Jan. 10 after being on a pro tryout contract during training camp.
NOTES: Roslovic extended his point streak (four goals, five assists) to six games. … Blue Jackets forward Patrik Laine had two shots and one hit in 20:23 after being benched Monday in the final 26:19 of a 3-2 win against the Carolina Hurricanes. … Kane had his 90th regular-season three-point game, passing Jeremy Roenick for fourth among United States-born players in NHL history. ... Mitchell played his 15th NHL game, all this season. Beaudin played his eighth, seventh this season.