Philadelphia forward James van Riemsdyk blocked a shot in the first period and then headed off the ice with what was diagnosed with a broken bone in his left foot.
Team officials indicated after the game van Riemsdyk could be lost for at least six weeks. He has 11 goals and 13 assists this season.
The game was deadlocked at 2-2 when Jagr scored on a backhand shot with 11:02 to play in the second period. Read produced his second goal of the game less than a minute later.
Ilya Bryzgalov got the win by stopping 21-of-24 shots.
Evgeni Nabokov allowed five goals on 29 shots while the Islanders were suffering their third straight loss.
Read tipped in a shot midway through the first period to bring the Flyers back from an early 1-0 deficit. It was his first goal since Feb. 2.
Jagr's goal boosted his career point total to 1,643, moving him past Joe Sakic into eighth place on the NHL's all-time list.
Celebrity Breakups and divorces of 2014 [PHOTOS]