With the score tied 2-2 late in the second period and the Canadiens on the power play, Bozak stripped defenseman Andrei Markov of the puck at his own blue line, skated in alone on net and put a forehand shot past Carey Price.
Mason Raymond scored a key goal for a 4-2 lead in the third period while James van Riemsdyk and Dion Phaneuf also each scored for Toronto, which improved to 5-0-2 in its last seven season-opening games.
James Reimer turned aside 34 shots for the Leafs.
Lars Eller tallied two goals with an assist and Brendan Gallagher also scored for Montreal.
Price stopped 34-of-38 shots in the Habs' opener.