"In the neutral zone, we did a better job of getting speed and getting on the forecheck," Carolina's Jordan Staal said.
Boone Jenner scored for Columbus, which outshot the Hurricanes 19-0 in the third period.
Carolina jumped ahead at 3:41 on its first shot. Gerbe grabbed a loose puck that defenseman Fedor Tyutin couldn't handle on an odd-man rush and scored his 15th of the season from the right circle.
"When you score first, it's always important and gives you a little confidence," Khudobin said.
"I'm happy with the win. I would probably be more happy if I didn't get scored on with like a minute left. But we got the result, we won. That's most important for me."
The Hurricanes were close to a playoff spot on Feb. 7, but they entered Tuesday's game having lost nine of 12 and are likely to miss the postseason again.
The Blue Jackets are in a tight race in the Eastern Conference. They dropped a rare one at home, where they are 10-3-1 in their past 14.
"It seemed we had some pretty good quality chances," Columbus coach Todd Richards said. "We hit a couple posts (during the game). We had our opportunities. I think we were doing some things to create offense. We just weren't able to finish."
Early in the second period, Loktionov poked home his fifth to make it 2-0 on the power play -- and Carolina's eighth shot -- with Jenner in the box for delay of game. Bobrovksy stopped Harrison's point shot, which broke the stick of Columbus' Derek MacKenzie, propelling the blade into the slot, but defenseman Jack Johnson couldn't stop Loktionov.
"I think the second period we picked it up and basically we scored at the right time with timely goals," Muller said.
Columbus had chances the rest of the period but couldn't beat Khudobin, who made a nice stop on R.J. Umberger. The Blue Jackets took two more penalties in the period that tempered their momentum.
Then, with room down the right side, Dwyer scored his seventh at 17:20 on a slap shot from the right circle that beat Bobrovsky near side.
In the third period, Khudobin turned aside one shot after another until Jenner scored his 13th on a redirection with 50 seconds left.
"It's funny, we've been on the other end so many times this year outshooting teams and coming up short," Muller said. "Change it around tonight ,and your goalie wins the hockey game. I guess it balances it out."
The 47 shots for Columbus were a season high. ...The Hurricanes last won in Columbus on March 8, 2004, a span of four games. ... Blue Jackets LW Blake Comeau knocked Hurricanes D Ryan Murphy from the game in the first period with a hit into the glass. It was Comeau's first game since a two-game suspension for boarding Red Wings defenseman Brendan Smith. ... Hurricanes C Elias Lindholm and D Justin Faulk fell ill and were late scratches.