Dach, who played his first three NHL seasons with the Blackhawks before joining the Habs this summer, hit the target with a good shot from the glove side.
Nick Suzuki and Cole Caufield had scored in penalties ahead of him. The Canadian shooters were 3-in-3 against Arvid Soderblom.
Samuel Montembeault, making his second straight start despite Jake Allen being healthy, was beaten by Jonathan Toews and Andreas Athanasiou in a shootout. However, Patrick Kane missed his try against him.
Joel Edmundson and Suzuki also scored in regular time (11-9-1) for the Canadian, who has won three of his last four games. Sean Monahan had two assists and Montembeault had 30 stops.
Caleb Jones and Taylor Raddysh answered for the Blackhawks (6-10-4) who suffered their sixth straight loss. Soderblom made 21 saves.
Canada striker Juraj Slafkovsky was rocked in the third period when he was blocked by a hard shoulder from Jason Dickinson. He returned to the bench at the start of extra time.
The Canadian will take the collar next Tuesday by hosting the San Jose Sharks at Bell Center.
The last word at CH
Edmundson began hostilities by scoring on the game’s first shot on goal. With about three minutes remaining, he deflected a pass from Monahan into the goal.
Söderblom signaled twice in the first half with his mitten. He stole a clear goal from Josh Anderson on an overrun attack from Habs and pulled the gauntlet past Joel Armia a few minutes later.
Montembeault also shone in the first third. A shot from Connor Murphy missed the target, then the puck came forward on the other side. Max Domi was there but Montembeault reacted in time to frustrate the former Canada forward with his left block.
The Blackhawks leveled the game early in the second period. Jones scored after a long run in the visitors’ area punctuated by two missed Brendan Gallagher outings.
Suzuki immediately restarted the Canadian on the power play. The captain of the habs moved the ropes with a lively wrist toss from the side of the mitt.
Montembeault kept the Canadian’s lead thanks to good saves, especially against Kane during a Blackhawks power play.
Gallagher had a great opportunity to increase the gap before the second break. However, he missed the target when he shot a breakaway from the backhand. Armia and Monahan, in turn, reached the post.
The Canadiens missed a few opportunities in the third period to extend their lead. Christian Dvorak hit the post and Suzuki lost control of the puck at the last moment on a breakaway.
The Blackhawks eventually made the Canadian pay dearly for his lack of opportunism. Raddysh leveled the game with less than four minutes remaining in the third period, using a comeback to score on the power play.
The Canadian was not able to use a power play in overtime, but Dach finally played the heroes in the penalty shoot-out.
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