Zegras, who was acquired by the Flyers in a trade with the Anaheim Ducks on June 23, tied the game 3-3 on a power play with his second goal at 7:32 of the third period.
Christian Dvorak had a goal and an assist for Philadelphia (4-3-1). Samuel Ersson made 23 saves.
Marshall Warren had two assists in his NHL debut for New York (4-3-1), which had won four in a row. Ilya Sorokin made 23 saves.
Simon Holmstrom scored short-handed to give the Islanders a 1-0 lead at 9:51 of the first period. He intercepted a pass into the slot, took a return pass from Jean-Gabriel Pageau off the rush and scored over Ersson’s blocker.
Anthony Duclair made it 2-0 at 6:15 of the second period when he tapped in a pass through the slot from Warren, a Long Island native (Laurel Hollow, New York) who had been called up from Bridgeport of the American Hockey League on Thursday.
Dvorak cut it to 2-1 at 10:29. He left the puck for Matvei Michkov at New York’s blue line, skated to the net and was open to score off a pass from Zegras.
Zegras’ first goal with the Flyers tied it 2-2 at 1:54 of the third period. Dvorak was able to control a bouncing puck and passed back to Zegras, who scored from the bottom of the right face-off circle.
Maxim Tsyplakov put the Islanders back in front 3-2 at 4:21, redirecting Warren’s point shot.
But Zegras tied it 3-3 at 7:32, knocking a loose puck in the crease under Sorokin after Islanders defenseman Scott Mayfield was penalized for high-sticking.
Zegras scored low blocker on Sorokin in the second round of the shootout, and Michkov scored in the third round. Holmstrom scored in the second round for New York.