The Flyers have won 23 of their last 24 against the Islanders.
Bobrovsky set the tone early by stopping a penalty shot by Michael Grabner just 2 minutes, 49 seconds into the game. Grabner earned the penalty shot after being pulled down from behind by all-star defenseman Kimmo Timonen.
The big saves continued throughout the game.
The Flyers were leading by 2-1 when Bobrovsky stopped Islanders center John Tavares on a one-timer from close range with 8:23 remaining in the third period.
With 4:25 left, the Flyers' Max Talbot was shaken up after being hit high by Steve Staios. Talbot stayed down briefly on the ice before going to the bench. No penalty was called, although Flyers coach Peter Laviolette had words for the officials.
Afterward, Talbot didn't hold back.
"That's what we're trying to stop in the NHL - shots like that head shot. I had no time to react," Talbot said. "I felt like the point of contact was my head. I didn't [see] the replay or anything, but from what I felt, it was a pretty dangerous hit. But we'll see what they say."
Staios was not made available to Philadelphia reporters.
The Flyers received a needed insurance goal when Talbot fed Sean Couturier, who sent a wrist shot in for his eighth goal of the season with just 1:30 to play.
"Max took a hit and chipped it out, and I was supporting him and picked up the pick, and it was a two-on-one, and the guy went down and I took a shot on the net," Couturier said.
New York made it 3-2 on Tavares' backhander with 15.7 seconds remaining.
Kyle Okposo had scored just 22 seconds into the third period for the Islanders, cutting the Flyers' lead to 2-1.
Standing alone in front of the net, Okposo tipped in a pass from Andrew MacDonald, who circled behind the goal to find his open teammate. It was Okposo's 10th goal of the season and got the Islanders as well as the crowd of 11,751 back into the game.
