"I've been a little bit snakebitten," Rasmussen said. "I've had quite a few chances. It was nice to get that one and get the win too."
By playing in his 10th game, Rasmussen, the No. 9 pick in the 2017 NHL Draft, fulfilled the first season of his three-year, entry-level contract and avoided being sent back to Tri-City of the Western Hockey League.
Larkin made it 2-0 with a shorthanded goal on a breakaway at 9:30. He outskated Columbus defenseman Seth Jones to the puck in the neutral zone. Jones lunged but couldn't pry the puck away, and Larkin slipped it through Joonas Korpisalo's pads.
"I was getting some puck luck in the first," Larkin said. "Pucks were bouncing on our sticks and we were going down on 2-on-1s and 3-on-1s.
"It was an open game. There was a lot of back and forth. It was an exciting game and we traded chance for chance."
Mantha scored at 13:33 to make it 3-0. Korpisalo was then pulled for Sergei Bobrovsky.
Korpisalo made four saves on seven shots in his third straight start; Bobrovsky made 23 saves on 24 shots.
"When the game feels like you're fighting it, especially early on, go back to the basics. Hitting, winning your battles, skating," Blue Jackets captain Nick Foligno said. "We didn't want to do that [in] the first period. It cost us."
Anderson made it 3-1 at 2:48 of the third and tied Cam Atkinson for the Blue Jackets lead with his sixth goal. Ryan Murray made a stretch pass to Markus Hannikainen, who dropped the puck to Anderson between the circles. Anderson whiffed on his initial shot before scoring.