Bryan Little had the winner.
It extended the Jets (10-9-2) winning streak to four and capped Philadelphia's at three.
The Jets came out fast and Byfuglien scored what for Winnipeg is a rarity — a power-play goal — just under four minutes into the first period, as he snapped the puck past a kneeling Steve Mason.
It was only Winnipeg's seventh power-play goal this season as the team sits 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 line with his glove.
And the Flyers took the lead a little over six minutes later on Simmonds' wrister from a goalmouth scramble just 13 seconds into Philadelphia's first power play of the game.
The second period was scoreless and like the first, the Flyers and Jets were tied on shots, 13-13 in the first and 9-9 in the second.
The Jets managed to up 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 blueline.
The Flyers managed only four shots in the third which went into overtime with the Jets ahead 35-26.
The Flyers put on a lot of heat, outshooting the Jets 8-3 during the four-on four, but couldn't get past Pavelec.
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 (5G, 8A) and Bryan Little (6G, 6A).