Philadelphia took advantage of Carolina's weak penalty-killing unit while improving to 13-3 in 2011. The Hurricanes were 23rd in the league against the power play entering Thursday's games, 25th on the road.
Carolina's Tuomo Ruutu was called for slashing late in the second period and Philadelphia made the most of the man advantage early in the third. Carter took a feed from Mike Richards and fired a wrist shot off Cam Ward's glove and in to make it 1-0.
Carter's sixth goal in five games, including three straight, gave him 26 on the season, temporarily tying him with Briere for the team lead. Briere went back in front at 11:27, going top shelf on the right side of the net.
Carolina had a quick response, ending Philadelphia's bid for its first shutout of the season. Ruutu poked in his own rebound at 12:07, picking up his first goal in 11 games and No. 13 for the season.
The Flyers are the only NHL team without a shutout, but still lead the Atlantic Division with 77 points.
Ward, the starting goalie in last week's All-Star game, continued to struggle against the Flyers, dropping to 3-8-2 in 13 career starts against Philadelphia. He was making his 14th straight start, and stopped 23 shots.
The Hurricanes haven't beaten the Flyers in regulation since 2006, when current Flyers coach Peter Laviolette was in charge of Carolina. The Hurricanes are 0-15-3 in the last 18 meetings.
NOTES: Ruutu played in his 250th career game. ... Carolina defenseman and former Flyer Joni Pitkanen was sidelined with a leg injury. ... Claude Giroux's assist on Briere's goal gave him at least one point in 10 of his last 11 games.