The Canadiens turned on the pressure early in the overtime when Tomas Plekanec skated in on a breakaway. Blackhawks goalie Corey Crawford made a kick save, but Chicago couldn't clear the zone and Plekanec just missed another chance.
Seconds later, the Habs attacked again and this time notched the game-winner when Markov converted a pass from Max Pacioretty with a shot from the left point.
Carey Price stopped 19-of-20 shots and Montreal picked up a third win in five games.
Marian Hossa got the only goal for the Hawks, who dropped a third straight.
Crawford finished with 36 saves.