"He even said he doesn't have to be seen much all game long, but he's that kind of player who steps up at the right time," winger Jake Voracek said. "That's why he's special."
For the second straight game, the Flyers blew a third-period lead, but this time, they managed to collect the much-needed two points. Briere's shot from the slot bounced off the right post and off goalie Cam Ward's lower back and into the net.
"I was planning on dropping it and decided to keep the puck, and it worked out," said Briere, whose team began the homestand with a 5-3 win over the Hurricanes a week earlier.
The Flyers finished the homestand with a 3-0-1 record, and they start a season-high, six-game road trip Monday in Toronto.
Defenseman Joe Corvo had tied it at 3 when his point drive caromed off Flyers defenseman Kurtis Foster and past goalie Ilya Bryzgalov with 12:02 left in the third period.
Carolina controlled most of the third period, outshooting the Flyers, 13-7.
"We were lucky to get into overtime," said Voracek, whose team has been outscored, 13-5, in third periods this season.
"We kind of sat back and let them take the play to us in the first 13, 14 minutes" of the third period, winger Matt Read said.
Just 15 seconds after Carolina tied the game at 2 on a seeing-eye shot by Jeff Skinner, Voracek tapped in a deft pass from Brayden Schenn (three points) to give the Flyers a 3-2 lead with 8:28 left in the second.
Corvo answered with his deflected third-period goal, setting up some tense moments near the finish, including a penalty kill by the Flyers that featured Bryzgalov's stop on Eric Staal.
It took Carolina all of 17 seconds to take a 1-0 lead as Jiri Tlusty scored on a juicy rebound allowed by Bryzgalov.
The Flyers dug out nicely, but not until after they squandered a 5-on-3 power play that lasted 1:30. One of the Carolina penalties was assessed to winger Tim Wallace, who received a five-minute boarding penalty and a game misconduct for sending rookie Tye McGinn into the glass. The game misconduct is automatic when a major penalty is called for a hit to the head.
With 6:08 left in the first, Schenn tipped Kimmo Timonen's point drive under the glove of Ward and to the far side, tying the score at 1-1.
Early in the second, Read gave the Flyers a 2-1 lead, scoring from the right circle after Staal's clearing attempt bounced off the skate of Mike Knuble. But Skinner tied it by circling behind the net and, from the right circle, somehow beating Bryzgalov to the short side as his shot appeared to go under the goalie's left armpit.
The Flyers won it in overtime, after Ward stopped Read on a last-second shot to end regulation.
"Danny's goal is something that can give us positive energy going into this road trip," Read said.
Contact Sam Carchidi at firstname.lastname@example.org. Follow on Twitter @BroadStBull.