Weal's goal came on only the second overtime shot for the Flyers after the Hurricanes dictated play for much of the extra session.
The center's seventh goal of the season ended his eight-game stretch without a point.
The Flyers improved to 6-9 in overtime results this season, while the Hurricanes fell to 5-9 in those situations.
Philadelphia goaltender Brian Elliott stopped 26 shots, including six in overtime. He was in his first game back after a four-game absence because of an injury.
Wayne Simmonds scored the Flyers' earlier goal.
Elias Lindholm scored for the Hurricanes, who dropped to 2-2-1 after crossing the midway mark of a season-long eight-game homestand.
Carolina goalie Cam Ward made 28 saves.
The Flyers and Hurricanes are both contending for one of the Eastern Conference playoff spots, though they both have ground to make up. This was the first of four scheduled meetings between the teams across a two-month span.
The Hurricanes didn't register a shot on goal in the opening 10 minutes of the third period. Then they had to kill off a two-minute Flyers power play.
Philadelphia registered seven of the nine shots on goal in the third period, but neither team scored.
Lindholm's goal came after Philadelphia's Nolan Patrick was sent to the penalty box for a double minor with 7:23 remaining in the first period. Lindholm tapped home his own rebound for his 15th goal of the season with 4:55 left in the period.
Teuvo Teravainen and Justin Faulk picked up assists on the goal.
Simmonds pulled the Flyers even with 3:17 remaining in the second period, tallying his 18th goal of the season. He showed his power by collecting a rebound and delivering it past Ward.
Jakub Voracek and Patrick recorded assists on the play.
Carolina has earned at least one point in nine of its past 10 home games against the Flyers.
--Field Level Media
Philadelphia | Carolina | |
Wayne Simmonds 1 | Points | Elias Lindholm 1 |
Wayne Simmonds 1 | Goals | Elias Lindholm 1 |
Valtteri Filppula 1 | Assists | Justin Faulk 1 |
N/A | Power Play Goals | Elias Lindholm 1 |
N/A | Short Handed Goals | N/A |
Brian Elliott .964 | Save Percentage | Cam Ward .933 |
Brian Elliott 27 | Saves | Cam Ward 28 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Philadelphia | 30 | 2 | 0-5 | 3-4 | 8 | 23 |
Carolina | 28 | 1 | 1-4 | 5-5 | 10 | 23 |