Marian Hossa tied the game inside the final minute with the extra attacker, then Sharp won it when his contested, rolling shot from between the circles rolled up Budaj's stick. Instead of trapping it, the Habs' netminder tried to shake it away, and the puck was propelled backwards and over the line.
Jeremy Morin also tallied and Corey Crawford came up with 28 saves for the Blackhawks, who moved two points back of idle Colorado for second place in the Central Division.
Dale Weise and Francis Bouillon scored for the Canadiens, while Budaj took the loss despite 25 stops. Montreal moved three points up on idle Tampa Bay for second in the Atlantic.