Bolduc scored five-hole on Daniil Tarasov for the first tally of the tie-breaker and Fowler turned aside Nate Danielson to deny a sixth straight Detroit attempt.
Fowler made 30 saves in his second straight start for Montreal (2-2-1), which had lost three straight (0-2-1).
Tarasov made 30 saves in his first start for Detroit (1-3-1), which lost 6-3 against the Seattle Kraken on Friday.
The Canadiens went 0-for-4 on the power play; Montreal has one power-play goal in 17 opportunities this season.
Fowler kept the game scoreless when he stuck out his left pad to make a save on Andrew Copp’s shot at 3:35 of the third period when the Red Wings forward drove in alone and went to his backhand.
Montreal had three goals waved off during the game, including the apparent winner Alexandre Texier at 2:37 of overtime. Bolduc, who had a goal disallowed in the second, was offside on the play.
An apparent goal by Cole Caufield was waved off at 1:16 of the first period. A video review determined that the puck had not completely crossed the goal line.
Another Canadiens goal by Bolduc was disallowed at 7:03 of the second period because Montreal forward Jake Evans interfered with Tarasov in the crease on the play.
