Kubina's third and fourth goals bookended tallies from Jeff O'Neill and captain Mats Sundin as the Leafs (23-21-6) played a tight defensive game in front of goalie Andrew Raycroft.
Tomas Plekanec had the lone goal for the Canadiens (27-18-5), who fell to fifth in the Eastern Conference after Ottawa's afternoon win over Boston pushed the Senators one point ahead of the Habs. The two clubs play Monday at Montreal.
The Canadiens seem to bring out the best in the Leafs, who improved to 3-0-2 on the season against their Original Six foes and have played some of their finest hockey of the season in those games.
On Saturday the Leafs were first on the puck and simply outworked and outskated the Canadiens, who looked flat in their first game after the all-star break. It's the kind of desperate hockey the Leafs will have to play as they try to stay in the playoff hunt in the second half. Montreal was one of nine teams ahead of Toronto in the Eastern Conference standings when play began Saturday and the win cut the gap between the two clubs to seven points. A Leafs loss would have made it 11 points.
Montreal's fourth-ranked penalty killing, meanwhile, didn't look terribly impressive on this night, the Leafs going 3-for-4 with the man advantage. The Habs went 1-for-7 on the power play.
The two clubs had 28 shots apiece before 19,508 at Air Canada Centre, many of them wearing Montreal jerseys.
The killer was Sundin's 19th goal of the season with 2:42 to go in the second period, giving Toronto a 3-1 lead, a power-play blast from the top of the faceoff circle that beat Cristobal Huet top corner on the stick side and took the wind out of Montreal's sails.
Kubina opened the scoring 13:29 into the second period with a slap shot from the point that beat a screened Huet inside the left post. O'Neill's goal 1:19 later needed a video review when it appeared Matt Stajan touched it with a high stick but it stood.
Plekanec gave the Habs hope when his wrist shot form the faceoff dot on a Montreal power play beat Raycroft top corner on the stick side 6:06 into the second period.
Kubina, who also had an assist, made it his first two-goal game as a Leaf with a powerful shot from the point 3:29 into the third period, a goal that put the game out of reach.
Notes: The Leafs begin a five-game road trip Tuesday night at Carolina with other stops in New York (Rangers), Ottawa, St. Louis and Nashville before returning home to host Sidney Crosby and the Pittsburgh Penguins on Feb. 10 ... Toronto remains without winger Darcy Tucker (foot, 1-2 weeks), forward Kyle Wellwood (hernia, seven weeks), centre Michael Peca (leg, indefinite) and defencemen Andy Wozniewski (shoulder, week to week) and Ian White (shoulder, day to day). White should be back Tuesday night.