Mitchell Marner had a goal and two assists, Auston Matthews scored twice, and William Nylander had three assists for the Maple Leafs (8-2-1), who are 5-0-1 in their past six games. Frederik Andersen made 16 saves.
"We were a rested team (their last game was a 4-3 overtime loss to the Edmonton Oilers on Jan. 30) playing against a very tired team who has had a very tough schedule," Maple Leafs coach Sheldon Keefe said. "So frankly, I expected us to be really good here today and make it hard on Vancouver. Now the challenge is to regroup and do it again (on Saturday)."
J.T. Miller had a goal and an assist, and Demko made 30 saves for the Canucks (6-8-0), who lost for the third time in four nights.
"I thought to be honest we looked like a tired team tonight playing against a fast, skilled team," Vancouver coach Travis Green said. "And we were a day late, a second behind everywhere on the ice. Not happy with the game. No one in that room is. That wasn't a good game. They're a good team. They're fast. They're skilled. When you're a step off and a step behind, they can make you look like we did tonight."
Miller cut it to 6-3 at 8:14 of the third, but Marner scored blocker-side at 11:37 for the 7-3 final.
"For us to feel sorry for ourselves and think it's going to come easy for us, it's not," Canucks captain Bo Horvat said. "It's not our goaltenders' fault. We give up too many Grade A opportunities. It's disappointing. I'm not going to sugarcoat it. We weren't good tonight."
Matthews gave Toronto a 1-0 lead at 2:56 of the first period when he cut around Miller and scored five-hole from in close. It was Matthews' sixth straight game with a goal and extended his point streak to eight games (eight goals, three assists).
Tanner Pearson tied it 1-1 at 6:24 when he jammed in a rebound at the side of the net. Spezza made it 2-1 with a power-play goal at 10:15.
"[Spezza] means a lot to this team, more than anybody knows," Matthews said. "That was fun to watch tonight, vintage Jason Spezza. He put on a show and he deserves it. He works so hard every day. At this stage of his career, the dedication he pours into his game and into the team is pretty incredible."