The Panthers center also added an assist for a three-point night and Sean Bergenheim contributed a goal and two assists as Florida vaulted two points ahead of the Winnipeg Jets for sole possession of first place in the Southeast Division.
Weiss' second goal came 4 minutes into the middle frame on the rebound of a Mikael Samuelsson shot and broke a 2-2 tie.
Scott Clemmensen earned the victory with 18 saves.
P.K. Subban and David Desharnais scored for Montreal, which stumbled to its fourth straight loss and sixth in seven games.
Peter Budaj made 28 saves for the Habs.
Ray Liotta sues skin care company over use of likeness
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