The Flyers erupted for three first-period goals, including two by Lecavalier, en route to their highest output of the season.
The Flyers were in danger of becoming the first NHL team not to score three goals in any of their first 10 games since the 1940-41 New York Americans, according to the Elias Sports Bureau.
Lecavalier, 33, completed his hat trick with 11 minutes, 7 seconds left, giving the Flyers (3-7) a 4-2 lead. As he was knocked down, he somehow swiped the puck to Claude Giroux, but he picked himself up in the slot and, while off-balance, knocked Giroux's return pass into an empty net before falling to the ice.
"It was a hardworking 15 seconds, probably the hardest he's worked since he's been a Flyer," winger Scott Hartnell said. "Not many players can do that."
For the Flyers, now 31-4-2 against the Islanders since 2007, there were numerous contributors:
Lecavalier, in his second game since returning from an injury, played right wing on Giroux's line and had his first hat trick since March 11, 2008, also against the Islanders.
Jake Voracek, who had a team-high 22 goals last season, had his first goal of the year.
Defenseman Mark Streit, returning to face his ex-teammates, contributed two first-period assists.
Giroux broke out of a slump with a pair of assists.
The Flyers had a total of 13 goals in their first nine games before Saturday.
Lecavalier (power play) and Voracek scored a minute apart early in the first period to give the Flyers a 2-0 lead - just their second two-goal advantage of the season.
Skating right to left, Voracek made a dazzling move around Matt Carkner and scored on a 12-footer from the slot for his first goal of the season.
"It's about time the puck went in," Voracek said.
Slowed by a back injury suffered in the preseason, Voracek showed the speed he displayed last season.
The Isles were coming off a draining, 4-3 comeback win in Pittsburgh the previous night.
"They played yesterday, so it was important for us to get off to a good start," Giroux said.
The Flyers were coming off a 2-1 win over the Rangers on Thursday.
"We're skating a lot better," Voracek said. "The last three or four games we've really picked up the pace. We've been creating a lot of offense and playing very responsible defensively."
With the Flyers holding a 2-1 lead, Lecavalier tapped in his own midair rebound past Kevin Poulin with 1:47 left in the opening period to give his team a two-goal cushion. Poulin was the second straight backup goalie to face the Flyers.
Late in the second period, Zac Rinaldo was hit in the face by teammate Braydon Coburn's shot. He received several stitches above his right eye and returned in the third period, and was called for a high-sticking penalty with 16:50 left.
The Flyers, aided by goalie Steve Mason, were 3 for 3 on the penalty kill.
"You count on goalie the most in the penalty kill," coach Craig Berube said, "and he came up with some huge saves at the right time."