Jenner's 5-on-3 goal 46 seconds into the second period gave Columbus a 3-1 lead. Laine's one-timer from the left circle hit the post and fell behind Daws, and Jenner was there to push it over the goal line.
Nico Hischier cut it to 3-2 at 16:00 with a snap shot from the right face-off circle.
Pavel Zacha scored a power-play goal at 7:06 of the third with a shot from the high slot for the 4-3 final.
"Most of the games, we have been down at some point," Laine said. "We've kind of struggled every now and then and been down in the game but we found our way back, always found way back in the game, found those goals. Proud of our team effort tonight."
NOTES:The Blue Jackets have won seven straight at home against the Devils and are 12-1-1 in their past 14 games against them; the regulation loss was Jan. 6 at New Jersey. … Columbus forward Brendan Gaunce left in the first period because of an upper-body injury. There was no update. … Blue Jackets defenseman Adam Boqvist (upper body) was unavailable and missed an opportunity to play against his brother, Devils forward Jesper Boqvist. … New Jersey scored in the first minute for the fifth time this season, which leads the NHL. … Blue Jackets forward Max Domi scored his 300th NHL point with an assist on Christiansen's goal. Domi has scored 99 goals with 201 assists in 473 games.