PHILADELPHIA -- At the end of last season, Sean Couturier asked Philadelphia Flyers management and the coaching staff for a bigger role for this season.

Through 34 games, the 25-year-old center already has set a career high in goals.

"He's doing everything that's asked of him," Flyers coach Dave Hakstol said after Couturier provided the game-winning goal in the Flyers' 4-3 win over the Detroit Red Wings on Wednesday night. "When he was a young player, he thrived with certain responsibilities in a defensive role, and as he's continued to grow, you're now seeing a player with added responsibility that is meeting that challenge and thriving under those expectations."

Claude Giroux picked up three assists, and Dale Weise, Wayne Simmonds and Robert Hagg also scored for the Flyers (15-12-7). Philadelphia won for the seventh time in eight games following a 10-game losing streak.

Flyers goaltender Brian Elliott made 25 saves in his ninth consecutive start to improve to 13-7-6.

Martin Frk, Mike Green and Gustav Nyquist scored for the Red Wings (13-14-7), who lost in regulation for the first time in five games (2-1-2). Jimmy Howard stopped 27 shots.

"We know that we're a pretty good team when we play the right way, and we've shown that," said Henrik Zetterberg, who picked up his 19th assist of the season. "Unfortunately, we haven't gotten all the points that we probably wanted in a lot of those games, but we've got to put this one away and focus on a big game in Boston (on Saturday)."

Couturier netted his game-winner 5:57 into the third period, snapping a 3-3 tie. He took a pass from Simmonds and jammed his own rebound under Howard for his team-high 16th goal. Couturier's previous career high of 15 goals came in 2014-15.

Giroux picked up an assist on that goal, giving him 39 points (13 goals, 26 assists) in his first 34 games. Last season, Giroux struggled through a 58-point campaign, his lowest point total since his first full NHL season.

"It got a little personal, yeah," Giroux said of the criticism he faced last summer. "I try not to read too many things, but there wasn't a lot of positive articles in the summer, and I took that as motivation. I wanted to push myself to be the best player I can be."

The Red Wings thought they were going to have a power play in the closing minutes when Philadelphia's Jakub Voracek was whistled for elbowing Andreas Athanasiou, but when Athanasiou was sent to the box for embellishment, the power play was negated.

"It's hard to say that Double A dove there," Zetterberg said. "That's a pretty (bad) statement from the ref."

After evenly dividing two goals in the first period, the Flyers and Red Wings twice exchanged leads in the second period to enter the third period locked in a 3-3 tie.

Detroit took leads of 2-1 and 3-2 on second-period goals by Green on the power play and Nyquist at even strength, but the Flyers fought back with goals from Simmonds on the power play and Hagg at even strength.

Green's fourth goal of the season was also his second in as many nights. It came with Jordan Weal serving a double-minor for high sticking Frans Nielsen. Simmonds netted his 11th goal of the season and fifth on the power play 4:58 later when he converted a pass from NHL assist leader Voracek, who picked up his 34th helper in his 34th game.

Nyquist restored the Wings' lead when he netted his 10th of the season on a strong move to the net, but the Flyers tied the score again on Hagg's first NHL goal, a blast from the point that darted through Detroit defenseman Trevor Daley and past Howard.

In the opening period, Elliott stopped Nyquist and Athanasiou on breakaways in the first six minutes before Weise gave the Flyers a 1-0 lead with his fourth goal of the season with 4:41 remaining in the period. Weise hunted down an errant point shot by defenseman Radko Gudas and beat Howard to the far post on a wraparound stuffer.

The Red Wings tied it with 1.3 seconds remaining in the period when Frk snapped a pass from Dylan Larkin inside the near post for his eighth goal of the season and his fourth on the power play.

"I think it was only a couple of seconds left and I was hoping (Larkin) would maybe shoot and maybe the rebound would come," Frk said. "He passed, and I was there and I knew I had to shoot it very quick, because I didn't know how many seconds were left. I was glad it went in."

NOTES: Red Wings D Luke Glendening appeared to injure his hand while blocking a shot in the first period and did not return. ... Flyers LW Taylor Leier (upper body) sat out his first game because of injury this season. Leier had played in 28 of Philadelphia's first 33 games and had one goal and three assists. He was replaced by LW Jori Lehtera, who had been a healthy scratch the previous seven games. ... The Red Wings continue their four-game road trip Saturday in Boston, return home for Christmas, then head to New Jersey for a game Wednesday. ... The Flyers play their sixth set of back-to-back games Friday and Saturday when they visit the Buffalo Sabres and Columbus Blue Jackets. They are 2-2-1 in the front end and 2-2-1 in the back end. ... Scouts from the Golden Knights, Penguins, Blackhawks, Predators, Senators, Panthers, Blues, Stars and Islanders were in attendance prior to the NHL's midnight roster freeze.