Dan McGillis scored with 1:10 left in overtime for the winning goal, finishing off a 2-on-1 break with Daymond Langkow with a shot over goalie Arturs Irbe's glove.
The win stretched the Flyers unbeaten streak to seven games, all of it since Barber replaced Craig Ramsay as coach. It was their second straight win at home after they gained ties at Nashville, Colorado and Boston.
"We're spent right now," Barber said. "We've battled through some things on the road and we went through some time zones, too.
"We were getting a little short at the end. But this is another big step for our team."
The lastest victory wasn't pretty.
Carolina dominated play throughout most of the final period, swarming around the Philadelphia net. Goalie Roman Cechmanek, who stopped 35 shots, made a diving pad save on Ron Francis with seven minutes to play and then stopped Glen Wesley from the right point.
The Hurricanes outshot the Flyers, 10-6, in the third period and 32-21 in regulation.
Carolina, which beat the Flyers in their previous two meetings, dropped its third straight and fourth in its last six games.
Jeff O'Neill opeed the scoring with his 11th goal of the season blasting a shot from the top of the right circle past Cechmanek's stick side at 2:10 of the opening period.
"My eyes opened up as wide as a dinner plates," said O'Neill. "That kid (Cechmanek) played well. I thought we had some good chances to score but we just couldn't get it by him."
"It was one of those games where we didn't catch our breaks," added Irbe, who made 24 saves and had defeated the Flyers in three of his last four starts against them.
"Roman was throwing his body in front of the pucks. Philly's defense didn't allow us those chances for the second and third shots."
Simon Gagne tied it at 1 when he flicked in a loose puck into an open net over Irbe at 1:07 of the second period. Irbe stopped a slap shot from the right circle from Rick Tocchet and made a diving stick save on Michal Sykora before the goal by Gagne's goal, who has scored in four of his last five games.
The goal snapped Irbe's shutout streak of 142:26 against the Flyers. Irbe had shut out Philadelphia in three of his last four outings.
The Flyers will begin their longest road trip, a five-gamer, beginning at Florida Wednesday night, and they have 14 of their 18 games in January on the road.
"Right now, we're a team with no energy left in our dressing room," added Barber. "Just look at the nicks and cuts, and you know the team is playing the hardest it can play."
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