Briere has scored in each of his two games, and in four straight overall, since making a quick return following abdominal surgery.
He came back Saturday night after a six-game absence and put Philadelphia ahead 1-0 in that one, too, but the Flyers lost 2-1 to Tampa Bay.
The team said he had an unspecified lower body injury and wouldn't return.
Mike Richards gave Biron some breathing room by scoring a short-handed goal with 9:09 left to make it 2-0, and Kimmo Timonen added an empty-netter with 4 seconds remaining as Philadelphia snapped a three-game losing streak.
Biron took care of the rest, but fell 3:40 short of his first shutout of the season and 24th in his nine-season NHL career.
Trent Hunter cut New York's deficit to 2-1 by putting a shot between Biron's pads off a rush down the right side for his sixth goal this season, but not even the NHL debut of Josh Bailey could help the Islanders avoid their third straight loss (0-2-1). Joey MacDonald made 29 saves.
The 19-year-old Bailey, taken by New York with the ninth pick in this year's draft, hoped to crack the lineup long before 15th game of the season, but he was sidelined by a muscle strain since the preseason.
Now he will try to impress coach Scott Gordon enough that he doesn't get sent back to his junior hockey team.
Just 1:14 after the Flyers killed off a two-man disadvantage for the second time in the game - this one lasting a full two minutes - Briere gave Philadelphia a 1-0 lead. Skating near the right-wing boards, Briere waited for Islanders defenseman Brett Skinner to get in front of him and then used him as a screen. His shot from above the right circle beat MacDonald with 6:20 left in the middle period.
Richards came down on a 2-on-1 with Simon Gagne, while Philadelphia was short-handed for the eighth time, and got to a rebound of Gagne's shot to score his fifth.
Notes: For the second straight season, Powell dropped the ceremonial first puck at an Islanders home game. ... The Flyers were 0-4-3 in the previous seven games in which Briere played this season. ... Bailey was whistled for two of the Islanders' four penalties. He went off for hooking in the first period and high-sticking in the third.