Kurtis Foster, Brayden Coburn and Mike Knuble also scored for the Flyers, who won for just the third time in nine games.
Joni Pitkanen, Eric Staal and Patrick Dwyer had Carolina's goals.
Ilya Bryzgalov made several tough saves among his 39 stops and the Flyers continued their dominance over the Hurricanes. They are 23-4-4 against Carolina since Nov. 28, 2003.
Philadelphia scored three power-play goals on its first three chances. The Flyers came in 5 for 40 on the power play.
Playing just their third home game, the Flyers seemed energized in front of an orange-clad sellout crowd. They scored three goals in an action-filled first period and led the rest of the way.
Coburn and Briere scored 58 seconds apart for a 3-1 lead in the first. Coburn put one in after goalie Dan Ellis made a save on Jakub Voracek's breakaway shot. The rebound kicked out in front to Coburn, who slipped it into an open net.
With a man-advantage, Briere then redirected Giroux's shot from the side of the net for his first goal of the season.
But Carolina answered just 33 seconds later when Staal scored after picking up a loose puck following a turnover by Flyers defenseman Luke Schenn.
The Flyers regained their two-goal cushion just 52 seconds into the second when Knuble scored his first goal since rejoining Philadelphia last week after three seasons in Washington.
Matt Read forced a turnover behind the net on a poor clearing attempt by Justin Faulk. Knuble beat Ellis on a wraparound to send him to the bench. Ellis made 33 saves in a 1-0 victory over Ottawa on Friday night.
Giroux's power-play goal later in the second made it 5-2. Giroux snapped a six-game goal drought with his third of the season.
Dwyer slid one through after a perfect crossing pass from Jordan Staal to get Carolina within 5-3.
In a back-and-forth opening period, the Flyers scored first on Foster's power-play goal shortly after Bryzgalov made a save on a short-handed breakaway.
Read set it up by faking a shot and passing across to Foster at the right point. Foster skated in a few steps, wound up and fired a slap shot over Ellis' glove.
The Hurricanes tied it at 1 less than 4 minutes later when Pitkanen's slap shot beat Bryzgalov over his blocker.
Bryzgalov took a shot to the head from Jiri Tlusty in the final minutes, but finished the game after going down for a brief moment.