After three scoreless periods, the Avalanche finally struck for a goal in overtime.
McGinn, who was the closest Av to the play, earned the goal as Colorado won a third straight following a three-game losing streak.
Semyon Varlamov stopped all 19 shots he saw, notching his first shutout of the season.
Scrivens finished with 32 saves for Los Angeles, which dropped a second straight in overtime to complete a 1-0-2 homestand.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys