Lecavalier's tally off a Toronto turnover 9:25 into the game ended a streak of more than 154 scoreless minutes by Scrivens, who was coming off back-to-back shutouts for the Maple Leafs.
Benoit Pouliot had three assists for the Lightning, who posted a second straight win following a six-game skid.
Anders Lindback earned the victory with 23 saves.
Scrivens finished with nine saves on 13 shots while Jussi Rynnas made six saves in his first appearance of the season for the Leafs.
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