After Tomas Kaberle and Sergei Samsonov traded goals with the first shot of the shootout, goaltenders David Aebischer and Jean-Sebastien Aubin made five Saves each until Wellwood scored on a deke to the forehand and Aubin stopped Montreal's Alexander Perezhogin.
Kaberle, the target of critics this week, also had three goals in regulation time and assisted on Alexei Ponikarovsky's goal as the Leafs outshot Montreal 51-22, including 8-2 in overtime.
But after Toronto dominated for two and half periods, Samsonov's second goal of the game and a goal on a rocket shot from Sheldon Souray tied the score with 3:44 left in regulation time.
Perezhogin also scored for Montreal, which was outshot 19-5 in the second period, and outskated for most a one-sided match everywhere but the scoreboard.
The Leafs (5-4-3) were on the rebound from blowout losses of 6-2 and 7-2 to Ottawa. Montreal fell to 5-2-3.
The Leafs 4-2 lead in the third period looked safe until a shot off the end boards went to Samsonov's stick, and the skilled forward tucked it behind Aubin at 13:44.
With the sellout crowd of 21,273 in a steady roar, Mark Streit slipped the puck to Souray on the left point to move in and blast his sixth goal of the season past Aubin to tie the game and force overtime.
Kaberle, who had only two assists in the Leafs' first 11 games, assisted Ponikarovsky's power-play goal only 1:44 into the game.
After Saku Koivu slashed Michael Peca 30 seconds into the game, Ponikarovsky picked up a loose puck in the slot and shot into an open side on the power play.
A turnover in the Montreal end allowed Kaberle to fire a wrist shot past Aebischer at 4:50.
Samsonov, back on his regular line with Alex Kovalev and Tomas Plekanec after a two-game demotion to a checking trio, redirected a Streit pass behind Aubin at 7:39.
But Kaberle's backhand dribbled through Aebischer after some dogged work near the net by Darcy Tucker at 19:17.
A rare Montreal transition saw the speedy Perezhogin go around defenceman Ian White on a rush and slip the puck in the far corner at 10:39 of the second period.
Kaberle got that one back, too, at 12:05 when he threw the puck into a crowd in front and saw it sneak under Aebischer. The goal stood up after video review showed it was in.
It was Aubin's second start this season. He started in a 7-6 shootout loss in New Jersey on Oct. 12.
The win evened the series between the NHL's oldest rivals this season. Montreal defeated the Leafs in a shootout at the Air Canada Centre on Oct. 7. The teams split their eight meetings last season.
The Leafs, now 2-3 this season and 5-10 all-time in shootouts, return home to face Atlanta on Monday night while the Canadiens stay home to play Ottawa on Tuesday.
Notes - Nik Antropov returned to the Toronto lineup after missing the first 11 games with an ankle injury. . . . Forwards Wade Belak, Ben Ondrus and Alexander Suglobov were healthy scratches for the Leafs. . . . Montreal is missing D Mathieu Dandenault (leg), D Francis Bouillon (knee) and F Aaron Downey (concussion). . . . The Canadiens are 319-266-88 all-time against Toronto.