Their leading scorer, Jeff Skinner, is on injured reserve with a concussion, and perennial all-star captain Eric Staal has endured several lengthy scoring droughts.
The Hurricanes, who are last in the Eastern Conference, hope Friday night's win can help turn their season around.
Tuomo Ruutu tipped in Jay Harrison's slapshot in overtime to lift Carolina to a 2-1 victory over the Ottawa Senators.
"Tonight is the most complete game we've played, and I think it can be a model for us going forward," Harrison said.
Cam Ward made 22 saves for Carolina, which outshot the Senators 38-23, including 29-14 through the first two periods. But the Hurricanes had a tough time getting the puck past Craig Anderson.
"We had so many chances off the rebound, but we couldn't bury them," said Ruutu, who was denied on several opportunities in regulation.
The Hurricanes had not won an overtime game this season, including December extra-time outings under coach Kirk Muller, who replaced the fired Paul Maurice during the last week of November.
"We've been in this situation before, and it hasn't gone our way," Ward said. "It was rewarding to see the guys score there in overtime."
Muller said the game underscored his message to the players to keep pushing and pay attention to detail. Ruutu in particular seems to have gotten the message.
"I'm really happy they stayed with it. They pushed hard," Muller said. "It was great that Roots got it. He earned it because of the way he's been playing."
Carolina dominated the early play but couldn't capitalize often against Anderson, who stopped 36 shots. The Hurricanes had a 5-on-3 power play for 1:52 just past the midway point of the first period, but Anderson saved all their chances.
Andreas Nodl scored for Carolina less than three minutes in off the skate of an Ottawa defenceman. Nodl's goal was his second of the season — both coming in the last two games.
Filip Kuba countered for the Senators with 2:45 left in the first, sending a bouncing shot through Ward's legs.
The teams remained scoreless until overtime, when Ruutu got his stick on Harrison's blast 1:36 into the extra period.
Ottawa coach Paul MacLean said his team was sluggish after playing Thursday night at home, a 4-3 win over Florida.
"We didn't really generate a whole lot of offence consistently," MacLean said. "We played too much in our own end of the rink. . Overall, we're not happy with losing, but we can accept the point under the circumstances."
Before Ruutu's goal, the last time Carolina scored a 4-on-4 overtime goal to win was March 18 against the New York Islanders.
"We haven't been too successful in overtimes," Ruutu said. "Sometimes you gotta go 65 minutes, and that's what we did tonight. We have to keep going and remember how hard we worked tonight."
Ottawa fell to 5-5 this season in overtime games.
Notes: Tim Brent, Joni Pitkanen and Derek Joslin were scratches for Carolina. Ottawa's scratches were leading scorer Milan Michalek and defenceman Brian Lee. ... Ottawa won the previous two meetings this season, 3-2 in Raleigh in October and 4-3 in Ottawa in November. ... Carolina's Riley Nash, playing his second NHL game, recorded his first point with an assist on Nodl's goal. Nash was originally credited with the goal before replays showed otherwise.