Hunter scored for the first time in a month, and Jeff Tambellini and Sean Bergenheim added goals in the second period for the Islanders, who are tied for 12th in the Eastern Conference, and beat the Flyers for the first time in four meetings this season.
Ruslan Fedotenko scored with 5:58 to restore the Islanders' two-goal lead, before Joffrey Lupul cut it to 4-3 with 59.6 seconds remaining.
Rick DiPietro made 26 saves to win for the first time since Jan. 16 and send the injury-riddled Flyers to their fourth straight regulation loss.
Danny Briere and Scott Hartnell also scored for Philadelphia, missing forwards Simon Gagne and Scottie Upshall, and defenseman Braydon Coburn.
Antero Niittymaki stopped 43 shots in the loss.
The late-arriving crowd, delayed by a snowstorm, was entertained by the second-period offense and a talent show featuring wives of Islanders players on "Hockey and Heels" night.
Hunter broke the scoreless deadlock with 2:18 left in the first, netting his eighth of the season and first in 14 games. Josef Vasicek sent a shot in on goal that Niittymaki blocked, but didn't control. Ruslan Fedotenko crashed the net and took a jab at the puck in the crease before Hunter jammed it in from the left post.
New York racked up 17 shots in the period and faced only 11, despite giving Philadelphia two power plays without owning any.
One was doubly costly to the Islanders, who lost top defenseman Brendan Witt after a knee-to-knee collision with Hartnell in the neutral zone just past the 9-minute mark. Witt was whistled for tripping and then sidelined by a bruised knee.
Philadelphia needed only 50 seconds of its fourth power play to get even. Briere got two whacks at the puck at the left post before controlling hit behind the net. He fed Mike Knuble for a shot, then got the rebound and put it past a sprawled DiPietro for his 21st goal 1:05 into the second.
The rest of the period belonged to New York.
DiPietro kept it tied when Mike Richards raced in on a short-handed breakaway, forcing him to miss wide left about 3½ minutes into the period.
Tambellini then intercepted a pass from Flyers captain Jason Smith and wristed a shot under Niittymaki's right arm to put the Islanders in front 2-1 at 5:27.
New York nearly stretched its lead just past the midway mark of the period, but Smith went from defenseman to goalie after Niittymaki was out of position and blocked Tambellini's shot while on his side in front of the net.
He couldn't do anything about Bergenheim's breakaway goal after another turnover. Hunter sent a pass from New York's end to Bergenheim, who raced in front of defenseman Kimmo Timonen and bore down on Niittymaki.
Timonen hooked down Bergenheim, but the Islanders forward slung in a shot to make it 3-1 with 6:19 left.
Hartnell cut the Flyers' deficit to a goal at 17:30.
