Sam Reinhart, Jason Pominville, Ryan O'Reilly and Johan Larsson each had a goal and an assist, Rasmus Ristolainen had two assists, and Chad Johnson made 38 saves to lift the Sabres (21-34-11) to their third win in four games.
"This team can obviously beat anybody and any team can beat anyone, you just have to play the right way," said Johnson, who has won three straight starts, making the save on 93 of 98 shots (.949 save percentage). "Everybody has to buy in. It's not about one player on the team or anything like that. It's about a collective group, the five guys on the ice playing a certain way. It just shows we can beat anyone."
WATCH: [All Maple Leafs vs. Sabres highlights]
Leo Komarov scored twice, Mitchell Marner had a goal, and Frederik Andersen made 19 saves for the Maple Leafs, who are 0-2-2 in their past four games.
"It looked to me like we had the puck and we were controlling the play, and when they fired at the net, it hit off something and went in our net, and we couldn't keep it out of our net," Toronto coach Mike Babcock said. "Towards the end, we end up chasing the game and they played hard and we didn't get enough done."
The Maple Leafs (39-22-7) are three points behind the Boston Bruins for second place in the Atlantic Division, and Boston has five games in hand.
"We came out aggressive," Maple Leafs center Nazem Kadri said. "I thought we played well off the bat and had an all-around solid road period in the first. … A couple of unlucky breaks and deflections in front, and it costs you the game."
Reinhart gave the Sabres a 1-0 lead at 1:53 of the first period when he deflected a Ristolainen shot on the power play.
Pominville made it 2-0 1:50 later when he tipped a Ristolainen shot off Kadri's skate at 3:43.