Montreal's fourth line was on the ice for both goals, but it was a mistake by captain Shea Weber that opened the door for Toronto's first goal. Frederik Andersen got the win to improve to 25-11-2 after stopping 35 of 38 shots faced in the winning effort.
The Rangers are 1-2-1 entering the last leg of their five-game homestand and running out of time to make a playoff push, entering this contest nine points behind Pittsburgh for the second wild-card spot in the Eastern Conference. Montreal is third with 69 points.
The Canadiens had a four-minute power play midway through the period when Tavares was handed a double minor for high-sticking Jordie Benn.
If you were late getting to your seat or switching on the TV, you missed the game's first goal.
Lundqvist did not play in the first meeting between the teams and allowed 12 goals on 67 shots in two starts and three appearances against Toronto last season for a 7.06 goals-against average.
Tavares scored the victor with a backhand glove-side on Carey Price after taking a slick pass from Mitch Marner that crossed up Jeff Petry and Phillip Danault.
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Huawei shored up its lead after unit shipments soared 23.3 per cent, leading all major brands, according to IDC. The US-based company's revenue from the iPhone slid 15 percent in the October to December period.
Montreal finished 1 for 5 with the man advantage.
Zach Hyman stole the puck from Weber behind the net before finding Andreas Johnsson with a ideal backhanded cross-crease pass at 2:20 of the first.
Zaitsev gave Toronto a 2-1 lead at 4:42 with a wrist shot from the point on a pass along the boards from Par Lindholm.
"They were physical, they played right, they were competitive, they put the puck in, they got on the cycle", said Babcock. Tatar scored off a rush, beating Andersen with a rising shot to the glove side after taking a pass from Weber.
Sportsnet's Elliotte Friedman reported on Hockey Night in Canada's "Headlines" segment that while the Maple Leafs are exploring the rental market for help, they will not part with top defensive prospects and first-round selections Timothy Liljegren or Rasmus Sandin to land a potential impact player on an expiring deal. Earlier Saturday, the Canadiens acquired forward Dale Weise and defenceman Christian Folin from the Philadelphia Flyers in exchange for forward Byron Froese and defenceman David Schlemko.
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