Nylander, who missed the previous seven games with a groin injury, scored in the first round of the tiebreaker before Auston Matthews, who was stopped on a penalty shot with 1:14 left in overtime, scored the winner in the second round.
Max Domi scored the tying goal early in the third period, and Nicolas Roy also scored for the Maple Leafs (25-21-9), who had lost eight of nine (1-6-2). Joseph Woll made 28 saves.
Tom Willander and Jonathan Lekkerimaki scored for the Canucks (18-31-6), who have two wins in their past 17 games (2-12-3). Nikita Tolopilo made 39 saves.
Lekkerimaki gave Vancouver a 1-0 lead at 1:55 of the second period after receiving a pass off the left boards from Liam Ohgren and snapping a quick shot short side over Woll’s blocker from the top left hash mark. It was Lekkerimaki’s first goal since the season opener on Oct. 9 in his 11th game of the season.
Elias Pettersson appeared to extend the Canucks’ lead at 5:59 from the right face-off circle for a quick low shot, but Toronto successfully challenged for goaltender interference after video review confirmed Vancouver forward Conor Garland made contact with Woll in the crease, preventing him from recovering for the second shot.
Roy tied it 1-1 at 13:34 after Nicholas Robertson spun off Canucks defenseman Pierre-Olivier Joseph along the right boards before passing to Roy inside the top of the right circle for a one-timer that went past Tolopilo low on the far side.
Willander put Vancouver ahead 2-1 at 14:45, jumping into the rush for a cross-ice pass from Evander Kane off his skate to his stick before firing a quick shot back the other way under Woll’s blocker from just outside the right hash marks.
Domi tied it 2-2 at 2:32 of the third period after a scrambled face-off in the offensive zone. Domi retrieved the puck out of a battle and quickly snapped a shot from just below the left dot that hit Tolopilo in the right shoulder before bouncing up off his back and in.
Toronto defenseman Morgan Reilly left the game with an upper-body injury at 14:45 of the second period and did not return.
