Gionta was at the left post to put a rebound off the end boards into an open side for the game-winner.
Alex Galchenyuk also scored for the Canadiens (27-12-5), who had been outscored 18-8 in their three previous outings. Montreal swept their three-game season series with the Lightning.
Richard Panik and Vincent Lecavalier scored for Tampa Bay (17-22-4), who are winless in five and have only one victory in its last eight games. The Lightning ended a four-game road trip.
It was Montreal's first win since clinching a playoff spot last week.
The Canadiens had given up nine goals in the first period of their three previous games, but Carey Price's goal posts came to rescue this time as Teddy Purcell, Sami Salo and Vincent Lacavalier all hit the iron in a scoreless opening 20 minutes.
It was Montreal that took the lead 4:04 into the second as Galchenyuk was parked at the edge of the crease to slip in a bouncing pass from Brendan Gallagher. It was the rookie's sixth goal in his last eight games.
Gionta then redirected a Tomas Plekanec pass behind Ben Bishop after a turnover at the Tampa Bay blue-line at 15:05.
The Lightning took advantage of their first power play as Panik made a deft move to take in a Victor Hedman pass and lift over a sprawled Price at 17:36.
Lecavalier tied it 5:07 into the third when a Hedman shot deflected off some skates in front and left a wide opening for the Bolts' captain to score his 10th of the season.
Salo left early in the second period with an upper body injury and did not return.
Notes: Brandon Prust sat out and Michael Ryder returned to the lineup for Montreal. ... The Canadiens returned rookie Nathan Beaulieu to AHL Hamilton, fuelling speculation that Raphael Diaz is getting close to returning from a concussion. ... Tom Pyatt was scratched for Tampa Bay.