Bjugstad assisted on Brad Boyes' tie-breaking goal with three seconds left in the second period before scoring twice in the third to help the Panthers win for the second time in their last three games.
Brandon Pirri, who celebrated his 23rd birthday Thursday, potted Florida's other goal, while Roberto Luongo turned aside 27 shots in the triumph.
Tyler Bozak and Paul Ranger each scored once for Toronto, which has lost three straight games. Drew MacIntyre made his first NHL start between the pipes and stopped 33-of-37 shots in the setback.
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Nick Bjugstad posted his first two-goal game and finished with a career-high three points as the Florida Panthers picked up a 4-2 win over the Toronto Maple Leafs at BB&T Center.