Couturier scored in regulation and provided the only goal in a shootout as the Flyers beat the Toronto Maple Leafs 5-4 Wednesday night.
Radko Gudas, Travis Konecny and Ryan Hartman also scored for Philadelphia, which remained mathematically alive for a playoff berth. The Flyers moved within eight points of idle Montreal for the final playoff spot in the Eastern Conference with five regular-season games remaining.
''Whatever it is, the situation, I think everyone has pride in here,'' Couturier said. ''We want to win games. It's a lot more fun to win. Whatever happens here down the stretch we need to finish strong and build something here. Just push on in the same direction.''
After four Flyers missed in the shootout, Couturier deked to his forehand and beat Frederik Andersen. It was his third shootout goal in 21 tries.
Carter Hart secured Philadelphia's third win the last eight games when he stopped Nylander's attempt. In addition to the 20-year-old rookie not allowing a goal on five attempts in his first career tiebreaker, Hart made 38 saves in regulation.
It looked as if the Flyers had the game won in overtime when Travis Sanheim poked the puck over the goal line 2:34 into the extra period. But the officials disallowed the goal because they said the whistle had blown to stop play, even though Andersen never appeared to have control.
Philadelphia interim coach Scott Gordon liked the way his team kept competing after they were down 2-0 after the first period.
''There's got to be an element of character that always comes to the forefront,'' Gordon said. ''And I'd like to think that's how we'll finish out the season.''
Nylander evened it at 4 with 8:27 left in the third when his turnaround shot from the slot, following a turnover by Shayne Gostisbehere, went high over Hart.
Hartman had put Philadelphia ahead 4-3 with 11 minutes left in regulation. He took a pass from Scott Laughton from behind the net and scored with a shot between Andersen's legs from close range.
Matthews tied it at 3 by following his own miss and converting from a sharp angle 1:43 into the third.
The Flyers took a 3-2 lead with second-period goals from Konecny, Gudas and Couturier.
It was that 20-minute stretch that probably cost Toronto two points.
''I was disappointed in our second period,'' Maple Leafs coach Mike Babcock said. ''I thought we let ourselves down with that. There's no reason to be careless with the puck and not take care of it, there's just no reason, especially for a team that's trying to do what we're trying to do.''
Konecny's wrist shot on the break whizzed over Andersen's left shoulder 3:39 into the period, pulling Philadelphia within 2-1.
Gudas evened the score 3:36 later when his long wrist shot got past a screened Andersen. Couturier netted his 32nd of the season on a deflection of a shot by Sanheim with 4:14 left in the period to give Philadelphia a one-goal lead heading into the third.
Goals by Brown and Kadri gave Toronto a 2-0 lead after the first period.
NOTES: Leafs C Patrick Marleau tied Mark Recchi for fifth place all-time in games played with his 1,652nd regular-season appearance. . Toronto won the season series 2-1. All three games were high-scoring, with the Leafs winning both in Toronto 6-0 on Nov. 24 and 7-6 on March 15. ... Philadelphia improved to 3-1 in shootouts this season, while the Leafs lost in their first shootout of the season.
Maple Leafs: At Ottawa on Saturday.
Flyers: At Carolina on Saturday.
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