The Sabres held a 2-1 lead advantage in the third when Brayden Schenn and Scott Hartnell scored less than 3 minutes apart for a 3-2 lead.
Then with time winding down, Matt Read got control of the puck at the left post and fed a pass to Lecavalier, who found the net from the bottom of the circle for the game-winner.
Mason made 16 saves as Philadelphia broke a two-game skid.
Cody Hodgson and Matt D'Agostini scored for Buffalo, which lost at home in regulation for the first time in nine games.
Jhonas Enroth stopped 29 shots.