Gagne scored his second goal of the game 48 seconds into overtime and the Flyers won their fifth straight game, 3-2 over the Carolina Hurricanes on Saturday.
"It's always fun when you get the winning goal," said Gagne. "There's no better feeling than when you see the puck crossing the red line and you know that's made the difference at the end. You get two points and you win the game."
Mike Richards also scored for the Flyers, who won their fourth straight at home. The Flyers had not won five straight games since Dec. 22-29, 2005.
"To think we'd be 6-1 at this point, I don't think anybody expected that," said Flyers coach John Stevens.
"It's a terrible way to end it," said Williams. "Back to back overtime losses, which make it three on the year, and we've only played eight on nine games. We've got to find ways to win these overtime games."
Gagne stopped a pass from Derian Hatcher with his skate, then snapped the game-winner into the net. It was his 400th career point.
Williams, an ex-Flyer who leads the Hurricanes with 11 points (3 goals, 8 assists), gave the Hurricanes a 2-1 lead with 2:08 left in the second period. He deflected Cory Stillman's shot from near the boards between the pads of goalie Martin Biron.
Richards pulled the Flyers even at 2-2 a minute and a half into the third period with a slapshot from the top of the right circle on a power play.
Staal made it 1-1 with a power play goal 46 seconds later, lifting the puck into the net from left of the crease after taking a cross-ice pass from Jeffrey Hamilton.
Staal's goal snapped Biron's shutout streak at 143 minutes and 20 seconds, dating back to a 3-1 win over the Islanders on Oct. 13.
Biron, who has started all seven Flyers games, had blanked Atlanta and New Jersey, both 4-0, in his previous two starts.
Biron was almost as sharp on Saturday, stopping 40 of 42 Carolina shots while improving his record to 6-1. Grahame had 28 saves.
"We want to show teams that we can come back," said Biron. "It's tough in this league to win when you're down after two periods. It's something that we take pride in doing."
- The Hurricanes completed a six-game road trip with a 3-1-2 record.
- Carolina LW Erik Cole was scratched because of a foot injury.
- The Flyers had stopped 13 straight power plays at home before Staal's first period goal.
- Staal leads the Hurricanes with six goals.