Mike Blunden and Max Pacioretty each scored in 1, on Saturday.
Erik Cole also netted a goal for Montreal, while Carey Price stopped 23-of-24 shots as the Canadiens won consecutive games for the first time under head coach Randy Cunneyworth.
Cunneyworth has led Montreal to a 3-6 record after replacing the fired Jacques Martin last month.
Vincent Lecavalier scored the lone goal for the Lightning, losers of three straight.
Mathieu Garon allowed all three goals on 28 shots.