Bozek, the third and final shooter for the Maple Leafs, notched the game-winning tally by wristing a shot past the glove of Vancouver goalie Jacob Markstrom. Toronto goalie Frederik Andersen subsequently closed the door on Thomas Vanek's effort, ending the shootout.
The Maple Leafs (25-16-2) trailed by a 2-0 count as the third period neared the midway point, but they found their offense just in time before the Air Canada Centre faithful.
Auston Matthews cued the comeback just a couple of minutes after the visitors made it a two-goal game when he finished a perfectly executed two-on-one rush with Zach Hyman by tucking a shot just inside the post at 8:23.
Bozek then converted his own rebound at 12:37 on a partial breakaway to even the game at 2-2 and force extra time.
The game also featured the NHL debut for Toronto defenseman Travis Dermott, a 2015 second-round draft pick who collected an assist in his first big-league game.
The loss, even if it came with a point in the standings, was the third straight for the Canucks (16-19-6). Vancouver has just two wins in its past 13 outings after letting one get away Saturday.
After a scoreless first period, Brock Boeser -- who leads all NHL rookies in goals and points -- opened the scoring early in the second period by ripping a short-side offering past Andersen for his 22nd goal of the season.
Sam Gagner doubled the Vancouver lead at 6:34 of the third period with a power-play goal during a five-on-three advantage.
Boeser thought he scored early in overtime when he ripped a shot that beat Andersen, but video replay showed it rang off both posts but didn't cross the line.
Andersen and Markstrom were each credited with 34 saves.
--Field Level Media
Vancouver | Toronto | |
Brock Boeser 1 | Points | Tyler Bozak 1 |
Brock Boeser 1 | Goals | Tyler Bozak 1 |
Daniel Sedin 1 | Assists | Travis Dermott 1 |
Sam Gagner 1 | Power Play Goals | N/A |
N/A | Short Handed Goals | N/A |
Jacob Markstrom .944 | Save Percentage | Frederik Andersen .944 |
Jacob Markstrom 34 | Saves | Frederik Andersen 34 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Vancouver | 36 | 2 | 1-3 | 4-4 | 8 | 26 |
Toronto | 36 | 3 | 0-4 | 2-3 | 6 | 45 |