Mitchell Marner and Justin Holl scored, and Jack Campbell made 32 saves for the Maple Leafs (51-21-7), who lost their second straight and had their lead on the Tampa Bay Lightning for second in the Atlantic Division cut to five points. Tampa Bay defeated the Nashville Predators 6-2 on Saturday.
Auston Matthews, who leads the NHL with 58 goals, had seven shots on goal and played 21:40 for the Maple Leafs after missing three games with an undisclosed injury.
"It didn't go too bad," Matthews said. "We created a lot of chances, but the bounces didn't go our way. I thought we did a lot of good things. Definitely would have liked to see us get that extra point."
Toronto, coming off an 8-1 loss to Tampa Bay on Thursday, took a 2-0 lead while outshooting Florida 13-8 in the first period.
Marner gave the Maple Leafs a 1-0 lead at 3:25 with a slap shot from the right face-off circle off TJ Brodie's dump-in that bounced off the end boards.
Holl made it 2-0 at 17:20 when his pass from the top of the right circle hit the stick of Bobrovsky and went in off the skate of Panthers defenseman Radko Gudas.
"I thought our guys played hard tonight," Maple Leafs coach Sheldon Keefe said. "We easily could have won the game. I thought we won the first and third period. Against this team, you've got to score more than two. That's what they've been doing all season, they find ways to win."
Barkov cut it to 2-1 at 6:26 of the second period on a rebound after Marchment split two Toronto defenders and drove to the net.