"Toronto was frustrating us, they played a tight-checking game,'' coach Gerard Gallant told the team website. "After that we played hard and held our composure.
"We had a great weekend and we didn't want a letdown."
Barkov tied the game early in the second period, hours after signing a six-year contract extension.
"It was a great day for me," Barkov told the Sun Sentinel. "A lot has happened today. I couldn't be any happier to be with this team for a long time and couldn't be any happier for the game."
The Panthers (29-15-5) reached the All-Star break in first place in the Atlantic Division. They finished 8-3-1 in January and are 15-3-1 in their past 19 games.
Toronto forward Nazem Kadri scored with 2:25 left in the first period and goaltender James Reimer finished with 22 saves for Toronto (17-21-9), which plays its final game before the break at the Tampa Bay Lightning on Wednesday.
"I thought we came out and played well," Reimer said. "Obviously, I think they had some Grade A chances, and they were able to get them by me. Sometimes, that's the way it goes, you know? We'll get back on the horse [Wednesday] and get after it."
The Panthers controlled play for most of the first period, outshooting the Maple Leafs 7-0 through the first 13:11. But Toronto capitalized on its first real scoring opportunity to take the lead.
Kadri took Peter Holland's bank pass off the boards as he came over the blue line, cut toward the middle after Florida defenseman Eric Gudbranson fell down, and swept across the front of the crease before tucking the puck past Luongo at 17:35 for his 10th of the season.
But the Panthers, who had been 0-9-2 this season when trailing after one period, took control in the second.
Barkov tied it at 3:49 with a power-play goal. With Phaneuf off for boarding, defenseman Brian Campbell's pass sent Barkov in alone. The third-year center, who signed a six-year contract extension earlier Tuesday, went forehand-to-backhand before lifting the puck over Reimer's pad for his 13th goal.
"I thought we had things going good and our penalty kill was going good, and then Barkov walked right down the middle," Toronto coach Mike Babcock said. "We didn't do our job or what we're supposed to do, what we talked about it in the meeting and the next thing you know, I thought they got going."