Laine, whose previous hat trick came Feb. 17 last season against Chicago, had gone scoreless in his last nine games. Vladislav Gavrikov also scored for the Blue Jackets, and Johnny Gaudreau and Jack Roslovic had two assists apiece.
''I feel like it's been a frustrating season overall,'' Laine said. ''It's not only because I haven't been scoring lately but losing's not fun. If we're winning and I'm struggling, I'm not going to be (upset). Winning's all that matters.''
Elvis Merzlikins made 25 saves for his first victory since Dec. 11.
''Amazing, especially how guys played,'' Merzlikins said. ''We're dead last but we're not quitting playing hockey. We played hard, we were blocking the shots and doing simple things.''
Olli Maatta, Jake Walman and Lucas Raymond scored third-period goals for the Red Wings, and Ville Husso made 21 saves. Detroit beat Winnipeg and Toronto to open its three-game homestand.
''There was no jump and no life on the bench,'' Detroit captain Dylan Larkin said about falling behind by four goals. ''We were just kind of looking around and waiting for something good to happen. That's disappointing after playing a good game (against Toronto).''
The Blue Jackets scored three goals in a 2:43 span during the first period.
Laine scored his first goal of the game just after the Blue Jackets killed off Gavrikov's penalty. Johnny Gaudreau set up Laine's one-time from the left circle.
Gavrikov scored his third goal this season on a backhander during a scramble around the net.
Laine's second goal came on a fortunate break. Roslovic's shot went wide of the net, bounced off the back boards and onto Laine's stick.
''It was fun to get those two early and kind of go from there,'' Laine said. ''We had a pretty good first two (periods) as a line and as a team. Kind of sat back a little bit in the third but just more happy about the two points right now.''
Laine completed his hat trick with a slap shot from the left side just 1:32 into the second period. He has 12 goals this season.
The Red Wings broke through when Mathieu Olivier inadvertently tipped the puck into his own net at 5:50 of the third. Maatta was credited with his fourth goal.
Walman made it 4-2 at 7:08 with his fifth goal.
Raymond's backhander with just over four minutes remaining pulled Detroit within a goal.
''We haven't been in this situation, to be open and honest,'' Columbus coach Brad Larsen said of playing with a lead. ''We haven't been in this situation all year but we got through it. This is a big step for this group. I thought we handled it very well. You know they're going to push. They got some juice. They came at us and we made a couple of mistakes. Again, we haven't been in this situation but we found a way.''
Larkin was disappointed that the Wings couldn't sweep their three-game homestand.
''That's kind of been the story this season, we win two or three, but we can't get the fourth and fifth and get on a nice run,'' he said.
Gaudreau has 22 points in 16 career games against the Red Wings. ... Roslovic notched his 100th point with the Blue Jackets when he assisted on Laine's first goal. ... The Red Wings won the first two games of the three-game series. ... Columbus is 7-0-0 when leading after two periods.
Blue Jackets: Host New York Rangers on Monday night.
Red Wings: At Colorado on Monday night.
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