The Jets extended their winning streak to four games and ended Philadelphia's at three. Devin Setoguchi scored in the first round of the shootout for Winnipeg.
Scott Hartnell and Wayne Simmonds scored for the Flyers. Claude Giroux scored in the second round of the shootout for Philadelphia.
The Jets came out fast and Byfuglien scored a power-play goal at 5:36 of the first period, as he snapped the puck past Steve Mason.
It was only Winnipeg's seventh power-play goal this season as the team is 30th in the NHL with the man advantage.
But the Flyers came back with Hartnell's wraparound at 6:25 that was ruled a goal after a review. Jets goalie Ondrej Pavelec appeared to move it past the goal line with his glove.
And the Flyers took the lead at 11:45 of the first on Simmonds' wrister from a goalmouth scramble just 13 seconds into Philadelphia's first power play of the game.
The second period was scoreless. The Flyers and Jets were tied on shots, 13-13 in the first and 9-9 in the second.
The Jets managed to increase the pressure in the third, drawing a penalty that let Byfuglien even things up with another power-play goal at 14:23, as he slapped one in from the blue line.
The Flyers managed only four shots in the third. The Flyers put on a lot of pressure in the overtime, outshooting the Jets 8-3 during the four-on four.
Notes: The Flyers hadn't won a game this season in which they didn't score the first goal. ... At the start of Friday's game, the Jets leading scorers at the MTS Centre were Andrew Ladd (five goals, eight assists) and Bryan Little (six goals, six assists).