Dylan Cozens had a goal and an assist, Owen Power and JJ Peterka each had two assists, and Craig Anderson made 25 saves for the Sabres (33-28-5), who had lost four straight (0-3-1) and six of seven (1-5-1).
Buffalo trails the New York Islanders, who have played two more games, by five points for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
"Tonight was important for us because we played really well the other night (2-1 overtime loss to the New York Rangers on Saturday) and didn't get a win and didn't get the reward of the work," Sabres coach Don Granato said. "We've talked a lot about the work being defending, defending the right way and playing the right way. Tonight it wasn't working on the scoreboard halfway through the game, but sticking with the process … again, the chatter on the bench, there was no emotion, no extra wasted energy anywhere. They were dialed in. This group knows they can score. We're trying to sell that other side to them and believe in that confidence. Obviously, it came through tonight."
Auston Matthews had a goal and two assists, Mitchell Marner had two assists, and Matt Murray made 25 saves for the Maple Leafs (40-18-8), who had won two in a row.
Toronto remained four points ahead of the Tampa Bay Lightning for second in the Atlantic Division with one game in hand.
"We got two goals early in the (second) period, puts us in a good spot," Maple Leafs coach Sheldon Keefe said. "I didn't think we took care of it very well from there and then just allowed it to snowball. When you don't exit out of your zone cleanly, they get rolling and they get momentum, and now you're tired and you can't play your game. ... I thought we played better in the third. Our second period was our worst period by far, maybe of the season to be honest."
Tuch tied it 2-2 at 3:39 of the third period with a one-timer from in front off a spinning backhand pass from Tage Thompson, who fought off Jake McCabe below the goal line.