Brayden Schenn and Claude Giroux had goals in regulation for the Flyers, who snapped a scoreless drought that reached nearly 3 hours while earning just their third win in 14 games.
The Flyers were shut out in the previous two and entered averaging an NHL-worst 1.70 goals per game. They set a franchise low with only 34 goals through the first 20 games following Saturday's loss at Ottawa.
Victor Rask and Brett Pesce scored in the third period for the Hurricanes, who came back from a two-goal deficit to force overtime.
Rask was whistled for holding the stick 11 seconds into the extra session, and the Flyers took advantage.
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