Ponikarovsky's power-play goal with less than 7 minutes left in the first period put the Hurricanes ahead 1-0 and Jeff Skinner doubled the lead with his ninth of the season with 15 seconds remaining in the frame.
Cam Ward stopped 30-of-32 shots for Carolina, which won for the first time in seven visits to Philadelphia.
Matt Read scored a third-period power-play goal for the Flyers, who fell out of first place in the Atlantic Division with the loss.
Bryzgalov finished with 27 saves.
Millions of Getty images now available for free via embed tool
Boston schools pull out free condoms over wrapping complaints