With Florida on the power play and 7 minutes, 28 seconds left, goalie Brian Boucher stopped Mike Santorelli from in close, protecting the Flyers' 3-2 lead. The Panthers controlled play in the latter stages, but the Flyers held on for the victory.
After surrendering 41 shots in Saturday's come-from-ahead loss to Atlanta, the Flyers tightened their defense considerably. They allowed Florida just 23 shots.
The Flyers were coming off one of the most embarrassing losses in franchise history, Saturday's 5-4 overtime defeat to Atlanta, which trailed by two goals with three minutes left in regulation.
It was the first time since 1987 that the Flyers lost after taking at least a three-goal lead into the third period.
Perhaps incensed by that loss - and the fact that the Flyers had just four wins in their last 11 games - Laviolette shook up the lines, including the top unit of Danny Briere, Scott Hartnell, and Ville Leino, and the defensive pairings.
Laviolette started with an all-center line: Claude Giroux with Carter and Briere. He also had Mike Richards centering Hartnell and Leino; and Kris Versteeg centering James van Riemsdyk and Carcillo. The fourth line was familiar: Blair Betts centering Jody Shelley and Darroll Powe.
The coach tried six defensive pairings in the opening period.
The changes didn't do much in the first period as Florida, one of the NHL's worst teams, built a 2-1 lead despite managing just seven shots. The period included a 55-second five-on-three power play that the Flyers squandered.
The Flyers, thanks to a slick maneuver by Richards, took an early 1-0 lead. Richards faked a shot from in close, drawing goalie Tomas Vokoun out of the net. He then fed Hartnell in the low slot, and he knocked his 20th goal into a goalie-vacated net.
Center Stephen Weiss scurried into the net, but Hartnell swatted the puck past him.
The Flyers continued an inexplicable pattern that has plagued them lately - giving up a goal shortly after they have taken the lead.
Less than three minutes after Hartnell scored, Weiss tied it on a blast from the left circle.
With 1:49 left in the first, Dmitry Kulikov's point drive, which may have deflected off Powe, went past goalie Boucher to give the Panthers a 2-1 lead.
The Flyers seemed lifeless until Carcillo decisioned Mike Duco in a fight with 16:14 remaining in the second period.
Just 57 seconds later, Vokoun allowed a soft goal, enabling the Flyers to tie it at 2-2.
Giroux made a nice play to keep the puck in the zone, and Carter's shot from the high slot went off Vokoun's glove and trickled into the net.
Laviolette, whose mastery of timeouts has become part of his coaching identity, asked for a stoppage with 4:44 to go in the second period. Seven seconds later, Carter finished off a backhand pass from Briere on a two-on-one, putting the Flyers ahead, 3-2.
Briere said there was some "confusion" with Florida's defensemen on the fastbreak play.
"I saw them jump down, I poked the puck, and when I looked up, there was nobody, so I just tried to get down as fast as I could," he said. "When I got to the blue line, I saw Jeff coming from the side, and I tried to suck their defenseman to me to chip it to him."
Contact staff writer Sam Carchidi at firstname.lastname@example.org. Follow on Twitter at www.twitter.com/BroadStBull.