Brayden Schenn scored two goals and Claude Giroux added one for the Flyers, who scored three on the power play. Evander Kane, Olli Jokinen and Alexander Burmistrov scored for the Jets, whose road-game winning streak ended at 2.
Flyers left wing Scott Hartnell, who had missed the last 16 games with a broken foot, was a last-minute addition to the team's lineup. Not even his surprise return was enough for the Flyers to hit the ice with any energy. They went a stretch of 9:47 in the opening period without registering a shot on Ondrej Pavelec.
Jets left wing Evander Kane scored the first goal of the afternoon, the third game in a row in which the Flyers were scored on first. Kane swatted home the puck as he stood unguarded to left of Flyers goaltender Ilya Bryzgalov.
Schenn answered back, stuffing the puck past Pavelec with just under 5 minutes left in the first period.
Jets center Jokinen broke the 1-1 second-period tie, after stealing the puck from Schenn as he charged into the Flyers' zone. Jokinen stopped only to spin around and lob the puck into the net.
Bryzgalov, who fought through fatigue, stopped 36 of 39 Jets shots.
Burmistrov's tip-in goal gave the Jets a 3-1 advantage, which at first appeared to be the enough his team would need to leave Philadelphia with a win. But the Flyers continued to fight to overcome their slow start - making their power play, which had struggled in recent games - count.
Giroux scored next to cut down the Jets' lead. During a long second-period Flyers 5 on 3, the Flyers' captain whipped the puck through traffic from the point, besting Pavelec, who stopped 33 of the 37 shots he faced.
Schenn tied the game at 6:18 into the third period, scoring his second of the afternoon and third in four games. And it was Schenn, once again, who set up the play that resulted in Simmonds' game winner at 8:47. Zac Rinaldo added an empty-net goal with a second left.