The Kings took a 1-0 lead when Austin Wagner scored with a sharp-angled shot into an open net at 14:22 of the first period. Francouz saved Nikolai Prokhorkin's initial shot, but the rebound took an awkward bounce to Wagner after it hit MacKinnon.
Anderson made it 2-0 at 15:25 of the first period when his shot from the right point was deflected in by defenseman Kevin Connauton. It was Anderson's first NHL point in his fifth game.
"Even though it wasn't the highlight reel he wanted, it was still a goal, and a goal is a goal," Wagner said. "They don't ask how, they ask how many, so we're all happy for him, and hopefully he can keep going."
The Avalanche, who were coming off a 4-3 win at the San Jose Sharks on Sunday, were outshot 11-4 in the first period.
"I thought we looked mentally tired," captain Gabriel Landeskog said. "I thought we were sloppy, especially in the first. … I liked the way we battled and I liked that we battled all the way to the end."
Pierre-Edouard Bellemare cut it to 2-1 at 2:19 of the third period when his wrist shot from the right point bounced over Quick's glove.
"They deserved those goals in the beginning, even if it was a lucky bounce. They worked for it," Bellemare said. "Then I feel like we could have packed it in and felt sorry for ourselves, but we battled all the way to the end."
Alex Iafallo put the Kings up 3-1 with a backhand on a breakaway at 14:35. He has six points (two goals, four assists) in the past five games.