Ryan Potulny and Kyle Calder scored early in the third period for the Flyers, who were outshot 42-19 but were opportunistic enough to pull out their second straight win. Philadelphia, which had lost 10 straight games before beating Tampa Bay and Carolina in the past week, sealed it with an empty-netter from Mike Knuble in the final minute.
Peter Forsberg also had three assists for the Flyers.
Ray Whitney scored twice for the Hurricanes, who generated plenty of scoring chances but struggled to put the puck past Esche.
It was an unlikely loss for the Hurricanes, who had won six of seven and were coming off a solid all-around effort in beating Anaheim - the NHL's best team - on Friday night. But instead of following up, the defending Stanley Cup champions stumbled to an embarrassing loss to the league's worst team.
With the score tied at 1, Forsberg corralled the puck deep in the zone and sent a pass to Todd Fedoruk as he skated toward the crease. The puck slipped through traffic to Zhitnik, who fired a shot past Cam Ward - who was bumped by Forsberg near the top of the crease - in the final seconds of the second period.
Philadelphia pushed the lead to 3-1 by taking advantage of a bad bounce along the boards. Instead of rolling around behind the net, the puck bounced out of the left corner and right to Fedoruk, who sent it Potulny for a goal against an out-of-position Ward early in the third.
Then - in a play that illustrated Philadelphia's opportunism - the Flyers grabbed a loose puck off a bad between-the-legs pass by Rod Brind'Amour on a Carolina push and got it ahead to Calder for a quick breakaway. Calder carried it all the way and beat Ward less than two minutes later for the 4-1 lead.
Whitney managed a goal off a loose rebound of a shot from Eric Belanger to make it 4-2 midway through the period, but Carolina got no closer.
Notes: Gagne's goal was his 20th of the season. ... Brind'Amour extended his scoring streak and has nine points in the past six games. ... Philadelphia C Jeff Carter extended his scoring streak to five games by assisting on Calder's breakaway. ... Belanger's assists on Whitney's goals was his first points in five games.