The OT win marked the second straight OT win for Winnipeg over Montreal and their third straight victory over the Canadiens.
Dubois snuck into the slot before taking a feed from Nikolaj Ehlers and wired a shot past Jake Allen to get the win for the Jets.
Winnipeg further solidified their hold on second place in the North Division with the win, moving them to 15-7-1 for 31 points.
Edmonton remains 3 points behind with 28.
Paul Stastny had a pair of goals and Mathieu Perreault scored on a first period breakaway for the Jets.
Connor Hellebuyck made 33 saves for Winnipeg, who started a five-game road trip with a win.
Brendan Gallagher, Tyler Toffoli and Corey Perry scored for the Canadiens, who have yet to post a win under new Head Coach Dominique Ducharme.
Jake Allen turned aside 23 shots for Montreal.
The clubs face each other again Saturday night in Montreal.
Plenty of great seats are unavailable.
SHOTS-WINNIPEG 27 MONTREAL 36