"It's been a challenge," Stamkos said about the plight of the Lightning, who have made a series of trades recently and are without several key players. "There's a lot of adversity we've had to overcome this last stretch."
Hall, however, helped pick up the slack. He added his second goal of the season for the Lightning, who are 11th in the Eastern Conference and trail eighth-place Washington by five points. Mathieu Garon finished with 23 saves.
"You never know when it's going to come," said Hall, a strong defensive forward. "Whether the points show it or not, you always find some way whether you're scoring goals or killing penalties or (winning) faceoffs."
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, last in the Eastern Conference, have lost five in a row, getting outscored 16-5.
"It's the worst feeling in the world," left wing Max Pacioretty said. "The mood is down, everyone's upset. It's definitely not fun. We've got to find a way to break out of this."
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, who was involved in the scrum, finished serving an interference penalty for making contact with Malone.
"He took care of his own business," Tampa Bay coach Guy Boucher said of Malone. "The blind hit he got there, that's extremely dangerous. The puck didn't even come close to him."
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.
"On the power play, you at least want to gain momentum," Pacioretty said. "But you heard their fans when they killed off that 5 minutes. It gave them momentum."
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.
"It was definitely a special feeling," Geoffrion said. "I was pumped for tonight. It's always disappointing to lose, obviously. Not a good feeling."
Geoffrion had a drive from the right circle stopped by Garon midway through the first.
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. Boucher said he was not feeling well, and added that the sick list also includes Malone and some of the assistant coaches.