McMillan's third-period scoring shot came from in front of the net with less than 9 minutes remaining. Ducks goalie Dan Ellis made it hold up, giving Anaheim life in the close Western Conference playoff hunt.
Ellis stopped 22-of-24 shots but got lucky when a desperation shot by Colorado's Milan Hejduk trickled over his shoulder only to hit the post and bounce out at the final buzzer.
Kevin Porter and David Jones scored, and Peter Budaj made 29 saves for the Avalanche.
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