Noah Cates had a goal and two assists, and Matvei Michkov had a goal and an assist for the Flyers (41-27-12), who have won four of five. Rasmus Ristolainen had two assists, and Dan Vladar made 28 saves.
Haydn Fleury scored the lone goal for the Jets (35-32-12), who had won three straight.
Connor Hellebuyck allowed five goals on 20 shots before he was replaced by Eric Comrie to begin the third period. Comrie made one save in relief.
Porter Martone gave the Flyers a 1-0 lead at 1:17 of the first period after stealing the puck from Jets forward Adam Lowry inside the defensive zone. Travis Konecny spun around in the high slot on the ensuing rush and passed to Martone, who scored with a sweeping one-timer at the left of the crease.
Winnipeg has allowed the first goal in six straight games.
Fleury tied it 1-1 at 6:57 when he lifted the rebound from a Cole Koepke wrist shot past Vladar's blocker.
Michkov put Philadelphia back up 2-1 at 8:24 with a wrist shot from just outside the top of the left face-off circle past the glove of Hellebuyck.
Couturier made it 3-1 just 25 seconds later at 8:49. He forced Fleury to turn the puck over, curled in the right circle and roofed a snap shot short side into the top corner.
Travis Sanheim extended the lead to 4-1 at 11:41 of the second period when his slap shot from the point trickled through Hellebuyck's five-hole.
Cates increased it to 5-1 with a short-handed goal at 19:28. He collected a pass from Christian Dvorak in the right circle and snapped the puck in off the left post. Dvorak's assist was his 300th NHL point (123 goals, 177 assists).
Couturier scored his second goal to make it 6-1 at 6:23, gathering a loose puck before going forehand-backhand in front and roofing it over a sprawling Comrie under the bar.
Nick Seeler scored at 13:32 on a wrist shot from the left circle under Comrie's right arm to secure the 7-1 final.
