Steve Mason made 25 saves in the victory, which put an end to the Flyers' two-game skid.
Scott Hartnell scored just 48 seconds into the contest and Couturier's backhander came 5:36 into the second.
The lone Winnipeg goal was produced by Michael Frolik with 7:07 to go in the third.
Ondrej Pavelec stopped 32-of-34 shots to take the loss. The Jets had won their previous two games and had been trying for what would have been their second three-game winning streak of the season.