Boyes scored a tiebreaking power-play goal in Florida's four-goal third period, sending the Panthers to a 6-4 victory over the Maple Leafs.
Willie Mitchell, Dmitry Kulikov and Scottie Upshall also scored in the third for the Panthers, who have won four of five. Jonathan Huberdeau had a goal and an assist, and Jussi Jokinen had two assists.
The Maple Leafs (20-13-3) were 14-0-0 when leading after two periods, but Florida (16-9-8) put an end to the streak in front of its season-best crowd of 17,877.
"We had a good chat between (the second and third) periods. We talked about getting back to our game and playing smart and a north-south game," Panthers coach Gerard Gallant said.
"We worked hard and we got a couple of bounces and breaks and I thought we deserved the game."
James van Riemsdyk had a goal and an assist for Toronto, which has dropped four of five. James Reimer made 29 saves.
Florida and Toronto combined for six goals in the second, but the Panthers controlled the final period.
Kulikov started the rally when he whistled a shot past Reimer 2:45 into the third for his first goal of the season. Mitchell, another defenceman, then used a pass from Huberdeau to tie it at 4.
"It was huge. It was a big gorilla (on my back); not a monkey," Kulikov said.
Boyes tipped in Kulikov's shot from the point for the game-winning goal at 16:45, and Upshall added an empty-netter for his fifth of the season.
"We just kept pounding away on them. We were throwing pucks at the net and making the most of our opportunities," Boyes said of his sixth goal.
"(Tonight) could be a message to us that we want to create more traffic in front of the net. Three of those (four) goals were the result of having scrums in front of the net."
Reimer said the traffic in front of him was an issue.
"They just got pucks and bodies to the net. Unfortunately, I wasn't able to see a couple of them and they got in the back of the net," he said.
Florida's closing flourish came after Roman Polak, van Riemsdyk and Nazem Kadri scored in a span of 4:42 in the second to lift the Maple Leafs to a 4-2 lead.
Polak beat goaltender Roberto Luongo on Toronto's ninth shot at 14:16. Van Riemsdyk then tipped a shot past Luongo at 17:30 after Cody Franson slid the puck between Florida defenceman Dylan Olsen's legs.
The power-play goal was van Riemsdyk's 16th of the season.
Joffrey Lupul led a 3-on-2 rush down the left wall and fed a pass to Kadri at 18:58, and the centre put it away for his 11th goal.
"We didn't put it away and couldn't keep the puck out of our net. I think everyone can share the blame in those goals in the third," Lupul said.
"When you're up 4-2 - that's a team that has trouble scoring, though they're a hard-working team - you've got to at least get a point out of that game."
Luongo finished with 13 stops.
"I didn't think we were very good and we had a 4-2 lead going into the third," Toronto coach Randy Carlyle said. "You should be able to take that home and play a solid enough 20 minutes to get yourself two points. That's the disappointing part."
Richard Panik, who scored Toronto's first goal on a wrist shot 6:38 into the second, left the game after a hit by Upshall and didn't return for the final period.
Huberdeau answered Panik's goal with a wrist shot at 8:24, and Jimmy Hayes gave Florida a 2-1 lead when he scored his 10th goal off a pass by Sean Bergenheim, who started the rush with a steal.
NOTES: Toronto brought up Christopher Gibson from Toronto of the AHL after starting goaltender Jonathan Bernier fell ill. Reimer was told Sunday morning he would start against Florida and said he was fine playing against Tampa Bay on Monday night. ... Carlyle became the 44th coach to reach 700 career NHL games. ... Toronto F Phil Kessel skated in his 400th game with the club. ... Luongo improved to 11-1-0 in his last 12 decisions against Toronto.