The Maple Leafs remained three points behind the Boston Bruins for second place in the Atlantic Division. The Bruins defeated the New Jersey Devils 1-0 on Saturday.
"I think we knew we were a lot better than the way we played (on Thursday in a 6-1 loss at the New York Islanders)," Tavares said. "We had a good day away from the rink on Friday, got some energy back and just tried to put the puck in deep and really try to wear them down and play a lot more in the offensive zone. We were a lot smarter with the puck through the neutral zone, especially with their transition game and the skilled guys they have."
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Nic Petan scored in his debut, and Frederik Andersen made 35 saves for the Maple Leafs (40-21-4), who are 4-1-0 in their past five games.
Jason Pominville and Conor Sheary scored, and Linus Ullmark made 27 saves for the Sabres (30-27-8), who have lost three of four and trail the Montreal Canadiens by nine points for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
"I'm not going to beat around the bush, it's disappointing we didn't get the result," Sabres coach Phil Housley said. "We didn't meet our standard tonight. But I like the way we played in the third period. I mean, these guys have fought and battled together, fought for each other in the third period. We get one goal, it changes the complexion of the game. But the bottom line is we just didn't get the result at this time of the year."