Mike Hoffman had a goal and an assist for Florida, which trailed 3-1 early in the third period. Mike Matheson had three assists, and Sergei Bobrovsky made 31 saves in the Panthers' seventh win in eight games.
Frederik Andersen started for Toronto and stopped seven of eight shots, but was forced into concussion protocol after getting bumped into at least three times - with the worst coming on a collision with Panthers center Frank Vatrano.
Coach Sheldon Keefe said his No. 1 goalie passed concussion protocol, but he didn't know if he would practice Tuesday before the Leafs fly to New York for a meeting with the Rangers on Wednesday.
''I don't think the result is in any way indicative of the way the game went,'' Keefe said. ''When you talk about the maturity of our team, a lot of the narrative is how we can't defend. That's the best defensive game we've played the entire season. I don't know if we gave up over four scoring chances at even-strength.
''(We) just got distracted by the 3-1 goal and perhaps that's an area we'd like to have back and do better job of. There's a lot of things to like about what we did.''
Matthews' 37th goal of the season made it 3-1 38 seconds into the third. But Pysyk and Huberdeau scored 58 seconds apart, tying it at 3 at 3:18.
Hoffman put the Panthers ahead to stay when he banked his 19th off Leafs defenseman Cody Ceci and through Hutchinson's pads at 10:30.
''It's just one of those series of unfortunate events that ends up in the back of your net,'' Hutchinson said.
Florida, which beat Toronto 8-4 in Sunrise on Jan. 12, weathered a late surge by the Maple Leafs before Pysyk completed his hat trick with an empty-netter.
''I got lucky at the end there,'' Pysyk said. ''Breakaway, open net. I thought I was going to miss it. ... I was a little nervous.''
The Panthers were without Aleksander Barkov, who was sidelined by a lower-body injury. The star center got hurt during Saturday's 4-0 loss at Montreal in Florida's first game back after the All-Star break and bye week.
Leafs defenseman Travis Dermott returned to the lineup after missing Saturday's 2-1 overtime win against Ottawa with an illness, while winger Kasperi Kapanen was also back following a one-game banishment to the press box for being late to Friday's practice.
NOTES: Florida D Anton Stralman, who was selected in the seventh round of the 2005 NHL draft by Toronto and played parts of two campaigns with the Leafs, suited up for the 800th regular-season game of his career.
Panthers: Visit Columbus on Tuesday.
Maple Leafs: Visit the New York Rangers on Wednesday.
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