Giguere improved to 8-2-1 in his last 11 games at the Staples Center, stopping all 13 shots he saw in the final period to help nail down the Avalanche's victory.
Cody McLeod and Peter Mueller scored 5 1/2 minutes apart in the second period to erase a 1-0 deficit for Colorado and Gabriel Landeskog added a power-play marker in the final frame to complete the scoring.
Jonathan Quick surrendered three goals on 31 shots for the Kings, who suffered only their second regulation loss in 16 games under new head Coach Darryl Sutter.
Anze Kopitar notched the only Los Angeles goal.
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