PHILADELPHIA -- Like many of his teammates, Shayne Gostisbehere struggled with his confidence during the Philadelphia Flyers' 10-game losing streak, going a minus-4 with eight penalty minutes during the slide.

The 24-year-old defenseman has been one of the Flyers' most impactful players since.

Gostisbehere scored a pair of power-play goals, including the game-winner 3:50 into overtime, to lead the Flyers to a 2-1 win over the Dallas Stars on Saturday night for their sixth straight victory. Gostisbehere has three goals, two assists and is plus-7 with no penalties during the winning streak.

"I think we are just feeding off of each other, finding lanes, and we were just relentless," said Gostisbehere, who leads all Flyers defensemen with six goals and 18 assists. "I think the goal at the end showed how we weren't giving up there."

Jakub Voracek picked up assists on both Gostisbehere's goals and goaltender Brian Elliott stopped 26 shots for the Flyers (14-11-7). Voracek leads the NHL with 33 assists.

Gemel Smith scored for the Stars (18-14-2), who have lost five of their last seven games (2-4-1).

"At the end of the day, we're not going to get any better until our impact players have a strong, positive impact in the game on a consistent basis," Stars coach Ken Hitchcock said. "We can't continue to have the role players on the hockey club carry the hockey club."

Hitchcock was referring to Tyler Seguin, who hit a post in overtime and has gone seven games without a goal, and Jamie Benn, who had no shots against the Flyers and has two goals in his last 14 games.

The Stars' struggles on the man-advantage also continued. They are now 2 of 40 in their last 14 games.

Hitchcock was also upset with veteran Alexander Radulov, who took a pair of penalties against the Flyers, including a hooking call against Valtteri Filppula that led to Gostisbheere's game-winner.

"It was two really poor penalties by a good player," Hitchcock said. "It's not team discipline, it's individual. He should talk to the team."

Radulov took full responsibility for the penalties.

"It's on me today," he said. "I got a little too emotional. Sometimes you get elbowed in the face and you don't get a call and you get frustrated. I took stupid penalties. I take responsibility for that and I'll make sure it doesn't happen again."

Ben Bishop stopped 28 shots in the loss to fall to 13-9-1. Bishop has lost three straight games but was sharp between the pipes. On the game-deciding goal, Bishop lost his stick and tried grabbing the stick of Flyers right winger Wayne Simmonds. Simmonds did not relent and leaped in the air to screen Bishop, who did not see Gostisbehere's blast from the left circle.

"I don't know what he was doing," Simmonds said. "If he wants to pull my stick he can pull it, but Ghost made an unbelievable shot there."

The loss delayed Hitchcock's pursuit of his 800th win. He is 799-488-113 with 88 ties. Only Scotty Bowman (1,244) and Joel Quenneville (867) have won more games.

Coming off a 5-2 loss in New Jersey 24 hours earlier, the Stars came out feisty. Captain Jamie Benn set the tone by roughing it up with Flyers captain Claude Giroux on the opening shift, which ended with both left wingers in the box with roughing minors.

The Stars controlled play through much of the first period and took a 1-0 lead at 7:13 on Smith's third goal of the season and first since Nov. 24. Fourth-line left winger Remi Elie used a burst of speed to beat Flyers defenseman Travis Sanheim to a loose puck and fed Smith, who beat Elliott from the right circle.

Philadelphia answered midway through the second period with a power-play goal by Gostisbehere. The Flyers pressured the Stars throughout the man-advantage and broke through when an errant shot by Voracek caromed to Gostisbehere, who scored as he was falling to the ice.

The goal was Gostisbehere's third on the power play. It was also the Flyers' first power-play goal in three games.

Bishop kept Dallas in the game by giving Voracek and Travis Konecny little room to score on two second-period breakaways. Both Philadelphia forwards shot wide after trying to deke Bishop.

The Stars' struggles on the man-advantage continued. They are 2 of 40 in their last 14 games.

NOTES: Stars D Marc Methot, sidelined since Nov. 6 with knee surgery, missed his 19th straight game. He is skating with the team and is expected to return to the lineup before Christmas. With Martin Hanzal (hamstring) and Antoine Roussel (elbow) back in the lineup, the Stars assigned C/LW Jason Dickinson to the AHL Texas Stars. ... Twenty-two of the Flyers' first 32 games have been against teams in the Western Conference. They have played against only four teams in their own Metropolitan Division. That trend continues Monday when former Flyers coach John Stevens brings his Los Angeles Kings to Philadelphia. The Flyers conclude their five-game homestand Wednesday against the Detroit Red Wings.