In regulation, Patrick Dwyer scored his first NHL goal at 15:00 of the second period, and Tuomo Ruutu scored 66 seconds later, giving Carolina a 2-1 advantage.
Regulation ended in a 2-2 deadlock after Philadelphia's Jeff Carter (power play) scored 46 seconds from the end.
Goalie Cam Ward stopped 24-of-26 shots for the Hurricanes, who lost the opener of the home-and-home series, 3-1, on Wednesday.
Carter and Joffrey Lupul both had a goal and an assist, while goaltender Martin Biron was beaten three times on 30 shots for the Flyers, whose six-game winning streak ended.
Despite the loss, the Flyers have won five of their last seven games against the Hurricanes.
On the power play, Carolina went 0-for-4, and Philadelphia scored twice in its four man-advantage chances.