Luke Schenn had the goal for the Flyers, who have opened the season 0-3-0 for the second year in a row. Before last year, Philadelphia had lost its first three games only one other time in franchise history.
Steve Mason made 32 saves for the Flyers.
The Hurricanes dominated large stretches of the opening period, taking advantage of a Philadelphia team that lost 4-1 at Montreal on Saturday night before travelling to Raleigh. For the period, Carolina outshot the Flyers 17-5.
Harrison opened the scoring with one of the Hurricanes' more benign opportunities, sneaking the puck through Mason's legs on a wrist shot from inside the blue line.
Philadelphia got that goal back 3:01 into the second period when Schenn skated around Carolina's Drayson Bowman and snapped the puck above Khudobin's left shoulder.
It was the Flyers' first even-strength goal of the season.
Dvorak gave the Hurricanes the lead for good when he scored a little more than 5 minutes later.
After Skinner deflected Schenn's clearing attempt, Dvorak collected the loose puck in the high slot. With Carolina's Riley Nash providing a screen, Dvorak's wrist shot beat Mason on the glove side.
Dvorak, who signed a free agent contract with the Hurricanes on Oct. 2 after coming to training camp on a tryout basis, also scored in the Hurricanes' season-opening loss to Detroit on Friday. The 18-year veteran had four goals in nine games for Anaheim last season.
The final period was a tight-checking affair with neither having many opportunities — Philadelphia managed only three shots.
NOTES: Elias Lindholm, Carolina's first-round draft pick, went to the Hurricanes' dressing room in the third period with an apparent injury to his right arm and did not return. . Philadelphia's Vincent Lecavalier came into the game having recorded 27 points in his last 27 games against the Hurricanes. . Mason had been undefeated in five career outings against Carolina.