Danny Briere scored two goals, Scott Hartnell had a goal and an assist, and Nikolay Zherdev and Mike Richards also scored for the Atlantic Division-leading Flyers.
They led 3-0 less than 2 minutes into the second period and cruised to their seventh win in eight games and their eighth straight over the Hurricanes.
Sergei Bobrovsky stopped 35 shots for Philadelphia.
Chad LaRose scored for Carolina, but Cam Ward allowed four goals and stopped only nine shots before he was pulled midway through the second period. Justin Peters finished, also making nine saves and giving up four goals.
The Hurricanes entered having won three straight home games by a combined 17-5. But they couldn't get anything going against Bobrovsky in the brief time this one was in doubt. Meanwhile, the rookie goalie got plenty of offensive support - especially from Carter - and had little trouble extending his team's dominance of the series.
Philadelphia, which had its six-game winning streak snapped four nights earlier with an overtime loss at Washington, improved to 14-0-3 in its last 17 meetings with Carolina.
Carter scored his first goal in the final minutes of the first - and 10 seconds into an unsportsmanlike conduct penalty on Erik Cole - when he sent a rebound past Ward and made it 2-0.
Carter extended the lead to three goals less than 2 minutes into the second when he redirected Andrej Meszaros' wrist shot from the circle - a goal that initially was credited to Meszaros.
Then, Carter ended Ward's night 4 minutes later when he skated up the boards and beat him with a quick wrist shot to his stick side with 14:02 left. That finished off his first hat trick since April 2009 against Toronto.
Briere scored the Flyers' first goal with 12:06 left in the first when he tapped in a cross-ice pass, then scored on a wrist shot midway through the third period to make it a six-goal game.
NOTES: Philadelphia RW Claude Giroux, who had two assists, has points in 12 of the Flyers' 16 games. ... Carolina RW Tom Kostopoulos and Philadelphia LW Daniel Carcillo dropped the gloves 20 seconds after Meszaros' goal. ... Carolina C Jiri Tlusty skated in his 100th career game.