Patrick Kane passed from the top of the left face-off circle to DeBrincat, who juggled the puck before batting it in off goalie Joonas Korpisalo's left arm.
"[Kane] was able to get it through, it bounced off my stick and I obviously wanted to put it toward the net," said DeBrincat, who has two overtime goals in his past four games. "It worked out this time, but pretty lucky."
Kane had two assists, and Kevin Lankinen made 29 saves for the Blackhawks (7-5-4), who are 5-1-1 in their past seven games.
"Big win for us, obviously, to respond and get two points," Chicago coach Jeremy Colliton said. "It was a battle. I liked our first period, thought we deserved better from the chances we created, a couple of really good power plays (0-for-2). As the game went on it tightened up, they had the lead and did a good job of making it hard for us to generate things. Missed opportunities, but I like how we stayed in it. We were one shot away and we continued to be one shot away until we got our chance."
Cam Atkinson had a goal and an assist, and Korpisalo made 28 saves for the Blue Jackets (7-5-4), who were coming off a 6-5 win here on Thursday.
"We got away from our style a little bit and they capitalized on those opportunities," Atkinson said. "It's nice that we got a point, but I think we should have come away with two."
Patrik Laine gave Columbus a 1-0 lead at 6:39 of the first period, taking a pass from Atkinson at center ice before scoring with a wrist shot from the top of the right circle that went in off the left post.
"That's how I'm getting my paychecks to do that, so it's just all natural," Laine said. "I'm not thinking about it, I'm just shooting it and I know I'm good at it."