Ryan Graves scored for the Avalanche (36-18-7), who have won three games in a row and six straight on the road. Joonas Donskoi scored the only goal of the tiebreaker in the bottom of the third round.
Colorado, which is 11-3-1 in its past 15 games, is one point behind the St. Louis Blues for first place in the Central Division.
"Just with all the guys we have out of the lineup, we have to check hard," Avalanche coach Jared Bednar said. "I just don't see us putting up a lot of goals with a bunch of the key guys missing. But you just got to stick with it. Stick with it, be a resilient team, and that's something we're going to need here down the stretch."
WATCH: [All Avalanche vs. Kings highlights]
Jonathan Quick made 30 saves for the Kings (22-34-6), who are 3-1-1 in their past five.
"It was a tough game to play," Los Angeles coach Todd McLellan said. "They really did a good job of checking, they got their sticks in lanes, deflected a lot of our shots, blocked a lot of our shots. Ended up being a bit of a frustrating night for us offensively."