Wojtek Wolski scored the Colorado goal and boosted the Avalanche to their fifth consecutive victory.
Theodore's shutout was the 25th of his career. Jonas Hiller allowed a goal on 30 shots.
Anaheim was blanked for the second straight night, having lost in Chicago 3-0.
Wolski's goal came on an odd-man rush with 8:01 remaining in the second period.
Theodore has won five consecutive starts, the first time he has done that in four seasons.
Anaheim won three of the four games the teams played this year and all four were decided by one goal.