Okposo's wrist shot with 2:58 to play in the third period tied the score 3-3. The power-play goal was his 20th of the season.
With both teams connecting on two of their first three tries in the shootout, Okposo scored on a backhand move to beat Roy Emery. Philadelphia goaltender Anders Nilsson, playing for the first time since Dec. 9, then stopped Sean Couturier's shot to seal the win.
Nilsson ended up with 26 saves but Philadelphia got to him for three second-period goals. Matt Read opened the scoring with a short-handed goal 1:26 into the second period and the Islanders' John Tavares, off assists by Okposo and Thomas Vanek, tied the score 8 minutes later when New York was again on the power play.
Only 2:04 after that, the Flyers went ahead again when Wayne Simmonds wristed a shot past Nilsson. Matt Read made the score 3-1 Philadelphia with a quick shot off a pass from Mark Streit.
Philadelphia peppered Nilsson with 43 shots, including 17 in the second period when Brock Nelson and Okposo each scored goals.
Scarlett Johansson steps out with fiance after pregnancy reveal
Jessica Simpson shares three-way kiss with friends in photo