Connor Brown, Mitchell Marner and Nazem Kadri scored for Toronto (10-5-0), which has won two in a row.
"I thought we started real good the first 10 minutes, and then I thought we got (to) fooling around with the puck and they showed us how fast they were," Maple Leafs coach Mike Babcock said. "I thought they really dominated the second period. We were lucky to get out of the second. I didn't mind our third."
Brown gave the Maple Leafs a 1-0 lead at 5:30 of the first period after he stole the puck in the slot from Nick Holden and beat Fleury glove side. Toronto had failed to score before the third period in its five previous home games.
"Yeah, you know odds are you're going to win the game if you get out to a lead, so it's important to have a good start and I thought we had a good start," Brown said. "It kind of fell off from the way we wanted to play, but it was nice to stick with it."