Mitchell Marner scored for the sixth straight game and had two assists for the Maple Leafs (28-10-3), who have won four in a row.
"I just find I'm getting into open spots and I'm not afraid to shoot it," Marner said. "Before, maybe I would hold on to it an extra second trying to find another play, but right now, when it touches my stick, I'm just trying to one-time it or grip it and rip it."
Jack Campbell allowed three goals on nine shots before being replaced in the first period by Petr Mrazek, who made 19 saves on 20 shots.
"Mainly (a reflection) on the team," Toronto coach Sheldon Keefe said. "The type of chances we give up that early in the game, you don't even give your goaltender a chance to get comfortable at all, so that's why I took him out when I did and called a timeout. A lot of what we talked about was the fact that what we had done to Jack here, not giving him a chance to get comfortable in the game. Instead, he's facing high-end shots, guys in alone, that's on us."
Jesper Boqvist had a goal and an assist, and Akira Schmid made 27 saves for the Devils (15-24-5), who have lost five in a row and eight of their past nine games (1-8-0). The Devils were playing without coach Lindy Ruff after his father, Leeson, died Friday.
"Extremely disappointing," said New Jersey assistant Alain Nasreddine, who coached in place of Ruff. "We put ourselves in a good position to win a game against a good team but came up short in the end. It was exactly what we talked about, taking care of the puck, and we did it, I would say, for most of the game, but a team like that, we gave them too many opportunities there at the end and they made us pay."
Jason Spezza took a pass from Mikheyev from behind the net and shot from the slot to cut the lead to 4-3 at 4:16 of the third period. The goal was his first since Dec. 4 (12 games).
Marner tied it 4-4 at 13:28 after receiving a pass from Matthews in the slot.
"I think just doing what we do best in the third period (helped turn the momentum), forechecking, getting pucks back, getting around the net and being on pursuit of the puck the whole third period there," Marner said. "But obviously, we know we have to do better in the first 40 and something we have to make sure we bring tomorrow."