Tavares took a pass from Mitchell Marner and put a backhand over goalie Carey Price's left arm for his Toronto-leading 33rd goal.
"It just happened fast," Tavares said. "I got some good speed, so I was able to get a bit of gap on the guy defending me there. And Mitch put it in the perfect spot, so I was able to kind of already start to plan ahead before I even got it. So I know he's going to challenge hard and it's a debate whether you want to be kind of patient and try to go around him.
"I just felt I could get it up quick enough and lucky enough I was able to, and I got a lot on it, so I was happy to see it go in."
WATCH: [All Maple Leafs vs. Canadiens highlights]
Frederik Andersen made 35 saves for the Maple Leafs (34-17-3), who won for the fifth time in six games (5-0-1). It was Toronto's sixth straight victory against Montreal, its longest winning streak against the Canadiens since it won six in a row from Dec. 6, 1950-Feb. 7, 1951.
Price's personal seven-game winning streak ended in his 600th NHL game, all for Montreal (31-18-7), which lost for the first time in four games and is 8-1-2 in its past 11. He made 28 saves.
"They've got depth, they're a pretty well-rounded team," said Price, who made 28 saves. "They use their speed and they obviously have a lot of skill up front."