Denis Gurianov increased the lead to 4-1 with a power-play goal at 11:30 after Laine was penalized for high-sticking him.
Radek Faksa made it 5-1 at 13:59, banking a backhand past Korpisalo, who was then replaced by Merzlikins.
"We struggled with the pace early on," Blue Jackets coach John Tortorella said. "They were a little quicker than we were, then I thought we got our legs underneath us.
"We had some real fluky goals go in, it's not on [Korpisalo], just some weird plays. We played better in the third period."
Grigorenko scored at 3:40 of the third to bring Columbus within 5-2, and Dean Kukan's goal at 7:23 made it 5-3.
"We were passing it around the outside a little too much," Laine said. "It looks great, but we're not creating any scoring chances. In the third, the guys tried to shoot the puck more."
Alexander Radulov scored into an empty net at 18:19 for the 6-3 final.
Although the first game didn't go as hoped, Laine said he is glad the debut is behind him.
"The whole game was tough. It was one of those games," he said. "It's about getting better game by game. I've had one morning skate with the team and that's it. So it's not the ideal situation."
NOTES: Laine's ice time was the most among Blue Jackets forwards. … Pavelski, 36, is the second-oldest Stars/Minnesota North Stars player to have multiple four-point games in a season (he had two goals and two assists in the season opener Jan. 22 against the Nashville Predators). Sergei Zubov was 37 in 2007-08. … Klingberg moved past Brad Maxwell into fourth place for points among Stars/North Stars defensemen. Zubov leads with 549. … Kukan's goal was his second in 88 NHL games in five seasons. He scored Dec. 13, 2019, against the Arizona Coyotes.