Flyers coach Peter Laviolette said Rinaldo's fight was a "huge bolt of energy" for players and coaches and "picked up the building."
Ilya Bryzgalov made 21 saves as the Flyers (4-6) notched their second straight win. They can get back to .500 by sweeping the two remaining games on the four-game homestand - Thursday against Florida and Saturday afternoon against Carolina.
Sestito, 25, who spent most of the night on a line with Max Talbot and Ruslan Fedotenko, took a feed from Jake Voracek and beat Anders Lindback on a clever backhand with 15 minutes, 35 seconds left in the second period to give the Flyers a 1-0 lead. It was his first goal since 2010, when he was with Columbus.
Voracek won a board battle with Steven Stamkos before sliding a long pass to Sestito, who took the puck in the left circle and then slipped the shot between Lindback's pads.
But blown coverage by defenseman Bruno Gervais left the Lightning's Benoit Pouliot all alone in front, and he scored the equalizer by going top shelf midway through the third period. Pouliot took a pass from Teddy Purcell, who was beyond the goal line and had a slew of orange jerseys in his face.
About three minutes later, Sestito, who overcame the mumps a few months ago, took a deft chip pass from Fedotenko and again beat Lindback with a backhander, giving the Flyers a 2-1 lead with 7:24 to go.
With 4:50 left, the Flyers adroitly killed Mike Knuble's slashing penalty, keeping the NHL's best power play without a shot during the two-minute sequence.
With the game scoreless, Bryzgalov stopped Stamkos on a one-timer from the slot with 3:08 left in the opening period. More clutch stops followed, including a spectacular save on rookie Cory Conacher - Bryzgalov swatted the in-tight shot over the net with his glove - with about 15:40 remaining in the third period.
"Right now, he's our best player," Flyers captain Claude Giroux said.
The Flyers played much better than they did in their 5-1 loss at Tampa Bay on Jan. 27. In that game, Michael Leighton was rusty in the net and the Flyers allowed two power-play goals.
Contact Sam Carchidi at firstname.lastname@example.org.