Matt Duchene had two assists, and David Rittich made 26 saves for the Predators (19-11-2), who were coming off a 5-3 loss at the Washington Capitals on Wednesday that ended a seven-game winning streak.
"We did a lot of really good things," Nashville coach John Hynes said. "I commend our guys' effort, the intensity in a back to back. I really liked our team, loved their competitiveness, liked the way we played.
"When you talk about identity, you watch tonight's game, by probably every statistical measure we certainly deserved to win. We didn't find a way to do it."
Michael McCarron, who was recalled from the taxi squad on Wednesday, scored his first of the season to give the Predators a 1-0 lead at 2:50 of the first period. He took a pass from Matt Luff on a 2-on-1 and shot glove side from the slot.
Jenner tied it 1-1 on a redirection at 6:26.
"It felt good to get some game action after a couple of weeks," Jenner said. "You want to get into it early, making some plays. The first two periods weren't as sharp as we wanted to be, we didn't do what we need to be successful. We pushed in the third and got the goal by [Alexandre] Texier, then the extra point."
Laine 24 seconds into the second period to give Columbus a 2-1 lead, finishing a give-and-go with Jakub Voracek.
"With what he's gone through with the injury and his father, I have no doubt that this was an emotional game for him, and I'm really happy for him," Blue Jackets coach Brad Larsen said.