Rantanen, who is second in the NHL in scoring with 73 points (23 goals, 50 assists), had two of Colorado's six goals on 10 shots in the second period.
"He had a lower-body tweak, so I just kept him out of the third period for precautionary reasons, wanted to make sure he's healthy for our next game," said Avalanche coach Jared Bednar, who expects Rantanen to play Monday against the Nashville Predators.
WATCH: [All Kings vs. Avalanche highlights]
Tyson Barrie had three assists, Gabriel Landeskog and Carl Soderberg each had a goal and an assist, and Semyon Varlamov made 30 saves for the Avalanche (22-18-8), who lost four of their previous five games and were 2-8-2 in their past 12.
"It was real easy for us to come in focused," Barrie said. "We know how bad we've been lately, and that's unacceptable for this group. We're a team that has a lot of pride. We had a lot to prove, and I think we did that. Now it will be a test for us to show that we can do it on a nightly basis."