Claude Giroux scored on a great deke for the only shootout goal for either team.
Giroux deflected the praise to Bobrovsky.
"In practice, no one can score on him," Giroux said. "Obviously, we have a lot of confidence in him in the shootout. I get mad at him, actually, in practice because I can't score on him. . . . You saw how good he is, and he's patient."
Bobrovsky made two stops in the shootout, and Kris Versteeg lost the puck as he tried to make a move.
At the break, the Flyers are just three points behind the first-place New York Rangers in the Atlantic Division. They have stayed in the race despite a slew of injuries and subpar goaltending by Ilya Bryzgalov (2.99 goals-against average, .895 save percentage).
"We're in great position right now," Giroux said.
The Flyers don't play again until Tuesday against visiting Winnipeg. That will give some of their injured players time to heal - and give the other Flyers a chance to get some rest after a productive 31/2-month stretch in which they went 29-14-5, including an NHL-best 18-7-2 road record.
Tomas Fleischmann fired a close shot off the left post while the Panthers were on the power play with a little more than six minutes remaining in regulation. A short time later, Bobrovsky stopped Marcel Goc on a deflection, perhaps his best save of the night.
The Flyers, playing their fifth game in eight days, outshot the Panthers, 37-25.
It marked the second consecutive shootout for the Flyers, who lost, 6-5, to Boston on Sunday with Bryzgalov in the nets. They have a 20-37 lifetime record in shootouts, including a 1-3 mark this season.
The Flyers played textbook defense in the second period, rarely allowing the Panthers to get a cycle working.
But Florida capitalized on the Flyers' lone defensive breakdown of the period and tied the score at 2 with 4 minutes, 20 seconds remaining in the second.
Caught out of position, the Flyers allowed the Panthers to break into the zone on a two-on-none. Former Flyer Versteeg waited, waited, waited . . . and then went past the goal and to the goal line, drawing Bobrovsky with him. Versteeg then dropped a back pass to Fleischmann, alone in front. Fleischmann spun around and put a backhander into the net, which was empty because Bobrovsky had overcommitted to Versteeg.
The Panthers, who slipped into second place behind Washington in the Southeast Division, took a 1-0 lead when Mikael Samuelsson blasted a shot past Bobrovsky on the power play after 2:49 of the first period. Bobrovsky had just made a pair of great stops against Stephen Weiss, but the rebound went to defenseman Brian Campbell, who sent a quick pass back to Samuelsson.
About eight minutes later, Schenn's shot flipped in the air and went off the back of goalie Scott Clemmensen and into the net. It crossed the goal line as the net was knocked off its moorings, causing a long video review.
The war room in Toronto ruled that the call on the ice would stand, so Schenn - whose father, Jeff, was at the game as part of the team's fathers-sons trip - was credited with his third goal, and the game was tied, 1-1. The goal made the Flyers 6 for 14 on the power play in their last three games.
"It's always nice to score in front of your dad," Schenn said.
The Flyers took a 2-1 lead as Jakub Voracek tipped in Tom Sestito's backhander from the right circle with 2:01 left in the opening period. It was Sestito's first point in five career games with the Flyers.
Contact staff writer Sam Carchidi at firstname.lastname@example.org or @BroadStBull on Twitter.