Adam Hall also scored for the Lightning, who are 11th in the Eastern Conference and trail eighth-place Washington by five points. Mathieu Garon finished with 23 saves.
Stamkos took a pass from Teddy Purcell, deked around goalie Carey Price and put the Lightning up 1-0 at 8:42 of the first period. Purcell, a game-time decision due to the flu, has 10 assists and 14 points during a career-high seven-game point streak.
Montreal got a goal from David Desharnais. The Canadiens have lost five in a row, getting outscored 16-5.
Tampa Bay went ahead 2-1 when Hall ended his 45-game goal drought, dating to the season opener Oct. 7 against Carolina, from the low slot off a pass from Ryan Malone 28 seconds into the second.
Desharnais had tied it at 1-all with 3:58 left in the first.
Malone was given an instigator penalty, 5-minute fighting major and a game misconduct at 8:16 of the second after a scuffle near the Canadiens bench. Montreal's Brad Staubitz got 2 minutes for interference from the bench and a 10-minute misconduct on the play.
The penalties came 20 seconds after Montreal's Alexei Emelin finished serving an interference penalty for making contact with Malone.
The Canadiens, who entered with the NHL's second-worst power play, failed to score on the ensuing 5-minute man advantage. Garon made an in-close save on Erik Cole, who had three strong scoring chances in the game.
Blake Geoffrion, recalled from Hamilton of the AHL on Monday, was scoreless in his Canadiens debut. The 24-year-old forward is the fourth generation of his family to play for Montreal. His great grandfather was Hall of Famer Howie Morenz. His paternal grandfather was Bernie "Boom Boom" Geoffrion, another NHL Hall of Famer. Geoffrion's father, Dan, played a season with the Habs.
Geoffrion had a drive from the right circle stopped by Garon midway through the first.
Notes: Canadiens great Jean Beliveau had a stroke Monday night for the second time in two years and is being treated at a Montreal hospital. ... The Lightning played without C Nate Thompson and D Brendan Mikkelson, who both have the flu.