Anze Kopitar scored for the Kings (20-16-5), who have been outscored 16-7 during a three-game losing streak. Jonathan Quick allowed three goals on 26 shots.
"Well, we played with them," Los Angeles coach Todd McLellan said. "I think last year at the end of the year, it wasn't a real game when we played against them, but we didn't have a lot of the pieces that we have right now. It was a competitive night, it was a hard night. I really believe we can play with any team in the League."
Kings center Quinton Byfield, the No. 2 pick in the 2020 NHL Draft, had three shots on goal and was 2-for-5 on face-offs in 15:00 of ice time in his season debut
The 19-year-old was expected to start this season with the Kings before fracturing his ankle in a preseason game Oct. 5.
"I think I was definitely a lot more comfortable," Byfield said. "Last year, it was still my first pro year, and it was kind of weird playing with all the people you grew up watching almost, you know, playing against all those guys. Now I just got a feeling I know I can play with them and contribute a little bit."
Rantanen gave Colorado a 1-0 lead at 9:43 of the first period. He got to the edge of the crease and redirected in Nathan MacKinnon's shot from the high slot at the end of a 1:13 shift for the first power-play unit.
Los Angeles is 6-for-11 on the penalty kill in its past four games.
"I don't have an explanation. Look, we would have addressed it a long time ago," McLellan said. "You take today's penalty kill, we win the face-off again. It's on our tape and we don't get the clear. And you don't get the clear, now you're tired."
Kiefer Sherwood made it 2-0 at 3:06 of the second period, scoring with a turnaround slap shot following a giveaway by Brendan Lemieux. It was his first goal since March 26, 2019, when he was a rookie for the Anaheim Ducks.