The Canadiens snapped a three-game losing streak and moved two points in front of Boston for the lead in the Northeast Division. Montreal, however, has only four games remaining in the regular season and the Bruins have six games to go.
Gionta's goal was his second of the game and came with Benoit Pouliot in the penalty box for holding.
Montreal had let a two-goal lead slip away before coming up with the game-winner from Gionta.
Alex Galchenyuk and Gionta both scored in the opening period, but Richard Panik cut the Lightning's deficit in half with 2:24 remaining in the first stanza. Vincent Lecavalier tied it early in the third.
Carey Price stopped 32-of-34 shots to get the win. The three Montreal goals came against Ben Bishop on 35 shots.
Tampa Bay has dropped five in a row to fall out of playoff contention.