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.
Celebrity Breakups and divorces of 2014 [PHOTOS]