Iginla nearly had another goal in the second period, but it was waved off for goaltender interference. He has 606 career NHL goals.
The winner was set up when Montreal defenceman P.K. Subban fell down near the blue line. On an odd-man-rush, Matt Duchene sent a pass over Mikhail Grigorenko, who then found a wide open Iginla in front of the net.
Erik Johnson also added a short-handed goal for the Avalanche, who picked up a needed home win. They're 1-3-1 at the Pepsi Center over their last five games.
Andrei Markov and Lars Eller scored for the Canadiens as they finish winless on a three-game trip.
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