Nikita Kucherov also scored for the Lightning (22-11-4), who have won the first two of a three-game homestand.
Killorn's goal at 4:53 of the third period gave the Lightning a 2-0 lead. He took a pass from Ryan Callahan at center ice and sent a snap shot between defensemen Tim Gleason and Michal Jordan and past goalie Cam Ward high on the glove side. It was Killorn's eighth goal of the season.
"It was nice to get one because after a while you grip your stick a little harder in hopes that something will happen," Killorn said. "[Gleason] provided a nice screen because I didn't even see the shot go in, I just heard the sound. He's a big man."
Carolina (10-21-4) struggled to get scoring opportunities for much of the game but Andrej Sekera made it 2-1 at 14:04 of the third period when he controlled the puck out of a scrum in front of the net and flipped the puck past goalie Ben Bishop.
"Unfortunately we got into some penalty trouble in the third and they were able to dictate play a little bit," Carolina defenseman John-Michael Liles said. "The chances we did generate I thought [Bishop] made some good stops."
Carolina tested Bishop in the opening minute of the game with an early scrum in front of the net in one of their few scoring opportunities, but the Hurricanes couldn't get off a clean shot.
Bishop had 25 saves in his first start since Dec. 15.
"It felt real good to get out there and get the win because they are a tough team regardless of their record," Bishop said. "I missed being out there a lot, you forget how much fun it is getting out there, especially in front of the home crowd."
The Hurricanes got stellar goaltending from Ward (36 saves), who kept the game close despite the Lightning's numerous opportunities in the scoring zone and six power plays. Ward's best save came when center Tyler Johnson had a look at an open net and Ward dove across the crease to deflect the shot with his glove.
"Yeah, Cam was good [and] he has been very solid for us all year," Carolina captain Eric Staal said. "I've known him for a long time and I know he's been very, very good this year. Like I said, it's been a tough go for us offensively to try to generate a little more and to try and create more offense and score some more goals. It feels like an uphill battle all year to try and get that offense going, but we'll keep working on it and get ready for the next game."
Kucherov scored his 15th goal of the season at 8:50 of the first period when he took a pass in the slot from Ondrej Palat and sent a one-timer past Ward high on the glove side.
"We played a full 60 minutes tonight and got the two points," Lightning forward Ryan Callahan said. "We can't exhale right now, the standings are too close and these games on home ice are too important. In the playoffs there are a lot of 2-1, 1-0 games that aren't always pretty, but [they are] games that you have to win."
"I thought we had a lot of really good chances to blow it open but we couldn't do it and sure enough, they come down and score," Lightning coach Jon Cooper said. "Give Carolina credit for pushing back and making it a one-goal game. We scored first, had the lead going into the third and won the game in regulation, so that's what we want to see."