Scott Hartnell, Wayne Simmonds and Sean Couturier scored for the Flyers (26-12-4), who moved within two points of the Atlantic Division-leading New York Rangers. Kyle Okposo and John Tavares scored for the Islanders.
The Flyers (26-12-4) have won 12 of 13 on Long Island during their dominant run against the Islanders. New York (15-20-6) had won three straight at home, including a 5-1 victory over Detroit on Tuesday.
Bobrovsky stopped Michael Grabner on a penalty shot 2:49 in and made a spectacular glove save on the Islanders right wing late in the second. The 23-year-old Russian has tormented the Islanders since joining the Flyers before last season. Bobrovsky (10-3-1) is 7-0 against New York.