Sparks was good after allowing two early goals in a 3-2 win over Pittsburgh last week, but allowed three goals on 29 shots in NY, including a soft Adam Mcquaid midway through the third period that all but ended any chance of a Toronto comeback.
Added Leafs goalie Frederik Andersen, who made 35 saves: "Over the last few days it was quite a build-up".
"It was a tight hockey game for the most part", said Tavares, who scored the victor 2:17 into overtime.
The Canadiens had a four-minute power play midway through the period when Tavares was handed a double minor for high-sticking Jordie Benn. "I was really excited to play the game and get going, and unfortunately we couldn't get the win".
It was the first meeting between Toronto and Montreal since the season opener, which the Leafs won 3-2 in overtime.
Tavares scored his 33rd goal of the season on a backhand shot from the slot after a pass from Mitch Marner.
"We had an opportunity in overtime to win in", said Price, who made 28 saves in his first loss since January 10.
Montreal finished 1 for 5 with the man advantage.
Just 51 seconds into Montreal's Hockey Day in Canada matchup with the Toronto Maple Leafs, Shaw netted his 12th goal of the season.
The Maple Leafs tied it at 2:20 when Johnsson poked in a rebound from Zach Hyman's wrap-around.
There haven't been many games like that, surprisingly, for the Leafs this season - nights when a power play that looks oh so good on paper strikes fear in an opposing penalty kill and decisively wins a game.
Having been knocked out of the playoffs by the Boston Bruins, who are notorious for their physical style, some believe the Toronto Maple Leafs need to "toughen up", and the fact they are looking at a Ferland-type player could suggest they feel the same, at least a little bit.
Nikita 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.
Montreal scored the equalizer 1:13 into the second period when Tatar surprised Andersen glove-side with a seemingly harmless, floating shot after carrying the puck from deep in his own zone.
The Canadiens made a trade earlier in the day, picking up forward Dale Weise and defenceman Christian Folin from Philadelphia in return for David Schlemko and Byron Froese.