Laine has scored 16 points (10 goals, six assists) during the streak.
"It's been a good streak so far," Laine said. "Obviously great that we're able to win games as a team. If I didn't have this streak going on and I'd be struggling and the team's winning, that's all that really matters. At the same time, it's nice to help out the guys and get some big points."
Boone Jenner had a goal and two assists, and Elvis Merzlikins made 28 saves for the Blue Jackets (24-23-1).
Seth Jones had an assist in a team-high 26:47 of ice time for the Blackhawks in his first game against his former team since the defenseman was acquired in a trade on July 23. Jones, who missed their game Jan. 11 in Columbus while in NHL COVID-19 protocol, scored 223 points (50 goals, 173 assists) in 381 games in six seasons with the Blue Jackets.
Ryan Carpenter and Philipp Kurashev each had a goal and an assist, and Arvid Soderblom made 30 saves in his third NHL game for the Blackhawks (18-25-7).
"We just had too many passengers at the start," Chicago coach Derek King said. "Guys were not ready to play and kind of easing their way into it and you can't do that when you have a young goalie in there. You have to be ready. We talked about it. You have to be ready when the puck drops, and we weren't, and the poor kid was left hanging out to dry. I mean, that's not very nice."