With time winding down in the extra frame, the Avalanche made one last rush into the Sharks' zone.
P.A. Parenteau launched a shot from the high slot that Antti Niemi blocked. The rebound, however, glanced off the skate of San Jose's Joe Pavelski directly to Duchene, who just beat the clock with a game-winning shot.
The Colorado center also scored in the first period.
Ryan O'Reilly added a goal for the Avalanche, who won a second straight after ending the Chicago Blackhawks' 24-game point streak Friday.
Semyon Varlamov made 36 saves to earn the victory.
Niemi finished with 39 saves.