Briere completed his first career hat trick from in-close with 7:39 left to play.
Buffalo also got a goal from Chris Drury, who has a four-game goal-scoring streak. The Sabres, coming off a 7-4 defeat to Washington on Saturday, have not lost consecutive games this season.
Vincent Lecavalier scored for the Lightning, who have lost four in a row. He has a goal in four straight games.