James van Riemsdyk also scored on the power play for the Flyers, and Claude Giroux had two assists.
The night got off to a fast start with the teams scoring three goals in the first seven minutes, two of them 1:53 apart.
Flyer goaltender Martin Jones, a Vancouver native, stopped 27 shots.
''He was an all-star tonight,'' Flyers head coach Alain Vigneault said. ''He played extremely well. He made the difference.''
Jones said it's always special to return to Vancouver and play at Rogers Arena, where his father, Harvey, was once vice president of arena operations.
''It's always fun to come home and play in front of family and friends,'' he said. ''I thought we played really well. The penalty kill was really good, we defended well.''
Couturier also praised Jones.
''In the second, and even in the third, he made some big saves late to keep us ahead, saved us a couple of times on the penalty kills,'' Couturier said. ''He was awesome and played a heck of a game.''
Quinn Hughes scored for the Canucks (3-4-1), tying the game just 1:55 after the Flyers opened the scoring. It was the sixth time in eight games Vancouver had given up the opening goal.
''It would be nice to go out there and score first,'' Hughes said. ''We didn't come out ready to play in the first. We had our chances, but it didn't go in for us.''
The Canucks' Jaroslav Halak stopped 26 shots.
''Power plays can't win the game all the time,'' Canuck forward Tanner Pearson said. ''You have to create a bit of something five-on-five.
''You have to have it right at the start.''
The Canucks had a chance with 1:20 remaining, when Flyer defenseman Ivan Provoro was called for tripping. With Halak pulled, Vancouver had a six-on-four advantage and managed two shots but couldn't score.
The Flyers, who had played the night before in Edmonton, showed more speed and controlled the puck early but the Canucks took over the play as the game progressed.
Philadelphia took advantage of a bad Vancouver pinch to score just 22 seconds into the first. Travis Konency got behind the Canuck defense and passed to Couturier who beat Halak on the far side.
Hughes tied the game at 2:15 with a shot from the blue line that looked to hit a Flyer defenseman and deflect past Jones.
Philadelphia took the lead again at 6:58, needing just 10 seconds to take advantage of Hughes being called for interference.
Giroux made a nice play, banking the puck off the back boards. Couturier picked up the puck and passed to van Riemsdyk, who scored into an open net.
The Canucks outshot the Flyers 16-5 in the second period but couldn't find the back of the net. Juho Lammikko had one of the best Vancouver chances after Jones stopped a shot. The rebound went to Lammikko on the doorstep. He got the shot away, but Jones made the save.
Soon after, Halak stopped Couturier who had a good scoring chance on a Philadelphia power play.
NOTES: The Canucks scored on their first shot of the game but were outshot 15-4 in the first period. Giroux has a point in each of Philadelphia's six games. . Vancouver registered their first win of the season against the Flyers, a 5-4 shootout road victory on Oct. 15. . Former Canuck Zack MacEwen had a spirited second-period fight with Luke Schenn. .. The Canucks played without defenseman Tucker Poolman, who left Tuesday lost against Minnesota with an upper body injury. . The Flyers defeated the Oilers in Edmonton 5-3 on Wednesday night. .. Philadelphia defenseman Keith Yandle played his 928th consecutive game. He last missed a regular season game in March 2009.
Philadelphia: At Calgary on Saturday night to wrap up its Canadian road trip.
Vancouver: Hosts Edmonton on Saturday night.
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