Briere, Kurtis Foster and Braydon Coburn each tallied in the first period while Giroux and Mike Knuble iced the contest with second-period scores for the Flyers, who halted a three-game losing streak.
Ilya Bryzgalov turned aside 39-of-42 shots for Philadelphia.
The Hurricanes got goals from Patrick Dwyer, Joni Pitkanen and Eric Staal but still fell for the second time in three contests.
Dan Ellis lasted until 6 minutes into the second period before he was pulled from the net, allowing four goals on just 12 shots.
Cam Ward mopped up with 11 saves for Carolina.