"We needed a win tonight," Florida defenceman Bryan McCabe said. "We needed to get that monkey off our back. We had a really solid effort tonight. I thought we competed much harder and played the way we needed to play to win."
Richard Zednik and Ville Peltonen also scored, and David Booth had two assists to help the Panthers end their losing streak and complete a season sweep of Toronto.
The Panthers hadn't swept Toronto since 1995-96, when they only faced each other twice.
"They've been struggling of late, having lost four," Toronto right wing Jamal Mayers said. "We knew that. We couldn't quite get that second goal to hopefully make them tighten up a little bit.
"But you've got to give their goalie credit, he played well."
Florida remained ninth in the Eastern Conference, a point behind Montreal and Carolina in the race for one of the eight playoff spots
The Panthers, coming off a 3-0 loss to Washington on Tuesday night in which they were held without a shot in the third period, haven't been to the playoffs since 2000.
"We're right back in the middle of the pack," Panthers coach Pete DeBoer said. "Hopefully, it gets us back mentally to a point where we can play the way we're capable of playing.
"And I think it will. I think it's exactly what we needed."
Mikhail Grabovski scored for Toronto, and Martin Gerber made 39 saves in the Leafs net.
"We had chances and we had good puck possession," Gerber said. "In the second period, we just lost the momentum and they were on top of us for a while. We had a tough time getting out of our zone.
"In the third, we tried everything we could. We had some chances, but we couldn't put it in."
Florida went up 2-1 on Zednik's goal at 6:21 in the second period.
Zednik took a pass from Booth and his shot went between the legs of Gerber as Toronto defenceman Andre Deveaux slid into his goalie. Peltonen made it 3-1 at 7:48 of the second with a backhander from the side of the net that trickled through Gerber's legs.
"In the second period, we got overwhelmed with some of their speed," Toronto coach Ron Wilson said. "Guys were just focused on the puck and not looking around. That can be a dangerous situation and it caught up to us."
Grabovski scored on a power play with 1:52 left in the first period to tie it at 1. Grabovski was near the crease when he one-timed a pass from Mayers from behind the net.
Weiss' goal at 7:15 in the first put the Panthers up 1-0. Weiss beat defenceman Anton Stralman, who lost his balance after being deked, and came in alone on Gerber.
Weiss put a backhander into the top of the net for his 12th goal of the season.
Weiss had two goals and four assists in Florida's three previous games against the Maple Leafs this season, but had not scored since March 1.
Notes: Florida had two shots in the first minute... The Panthers had 19 shots in the second period, one off their season high for shots in a period... Florida C Kamil Kreps limped off the ice in the second period after he became entangled with Toronto RW Jeff Hamilton and crashed skates-first into the boards. He later returned to game.