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.
Coming off a 2-1 win over Carolina on Tuesday, Bobrovsky improved to 7-0-0 in eight career games against the Islanders.
Scott Hartnell scored the game's first goal when he redirected a Jaromir Jagr wrist shot on the power play with 2:40 left in the first period. Hartnell has a team-high 19 goals.
Bobrovsky frustrated Grabner just past the midway point of the second period with a save even better than the one he made on the penalty shot. With Grabner skating in on a breakaway, Bobrovsky made a spectacular glove save on a backhander by the Islanders forward.
The Flyers extended their lead to 2-0 on an improbable goal by Wayne Simmonds. From behind the goal, Simmonds sent the puck into the crease, but it deflected off the skate of goalie Evgeni Nabokov and went in the short side of the goal with 6:52 left in the second period. It was Simmonds' 11th goal of the season and snapped a drought in which he had gone eight games without a goal.
Timonen got the assist when he sent the puck behind the net.
"I heard Hartsy [Hartnell] yelling back, 'Throw it,' so I just tried to throw it toward the net, and it went off Nabokov and went in the net," Simmonds said. "The goal definitely surprised me - I didn't think it went in."
Contact staff writer Marc Narducci at firstname.lastname@example.org, 856-779-3225, or @sjnard on Twitter.