Nathan MacKinnon also scored for the Avalanche, who held to recent form by continuing to pile up shots without getting many goals. Colorado had a 45-18 edge in shots.
The Avalanche outshot Arizona 46-14 on Wednesday and needed overtime for a 2-1 win.
``We talked a lot (Friday) morning that we need to bear down on the goal scoring,'' Rantanen said. ``We got some really good looks. I think it's confidence too. I think we're fighting it a little bit now scoring-wise, but we're playing well. With this team and this talent we know it's going to come soon.''
The Avalanche held their 15th straight opponent to fewer than 30 shots in a game, surpassing the mark set by the Stanley Cup winning team in 2000-01.
Calvin Petersen made a career high 44 saves for the Kings.
Petersen, activated from the NHL's COVID-19 list before the game, was sharp in his return. He made 32 saves through the first two periods and had to make several big saves.
``It was a bit of a surprise,'' Petersen said of being on the COVID-19 list. ``I got notified I was being put in protocol and had to wait it out, take it day by day and follow the protocol. By (Friday) morning I was able to get released back. I think it was a false positive. Glad to be back, I'm glad it was handled well and I was able to join the team.''
Rantanen broke through for Colorado midway through the second period when his shot from the point got through a screen by Gabriel Landeskog and beat Petersen at 9:18. It was his 13th goal of the season, which leads the team.
Los Angeles had two power-play chances in the final nine minutes and nearly scored on the second, but couldn't cash in. Petersen came off in the final two minutes and MacKinnon scored an empty-net goal at 18:37 to seal it.
``When you get a breakaway on the empty net you're always looking around first of all to see that there's nobody backchecking on you and you have teammates with you, so it's a pretty easy decision there just to give it to Nate,'' MacKinnon said.
The Kings juggled their lineup before the game, with defenceman Olli Maata entering the NHL COVID-19 protocol list and was placed on the non-roster list. Alex Iafallo was scratched with an illness, but he was not on the COVID-19 list. Defencemen Tobias Bjonfort and Daniel Brickley, forward Lias Andersson and goalie Troy Grosenick were recalled from the taxi squad.
Goalie Matt Villalta was put on the taxi squad and goaltender Jonathan Quick was put on the injured list.
``Today was a juggling act,'' Los Angeles coach Todd McLellan said. ``Someone asked me (Friday) morning if we're getting back to normalcy or getting close to it, and at that time I knew what was going on. There's no reason for us not to perform better, though.''
The teams meet again Sunday afternoon in Denver. The start time was moved up from 6 p.m. to 3:30 p.m. MST due to a snowstorm forecast to drop up to 2 feet in the metro area.