Nathan MacKinnon scored and Semyon Varlamov made 15 saves for the Avalanche (19-13-8), who have lost five straight games (0-4-1), tying their longest losing streak of the season, and are 2-6-3 in their past 11.
Colorado is 1-8 in games that ended past regulation this season.
"That can be the difference between getting into the [Stanley Cup Playoffs] and not getting into the playoffs," Avalanche coach Jared Bednar said. "They're big points. I give our team all the credit in the world for fighting back again tonight. It's not easy for us. It hasn't been an easy stretch for us to stay with it and come back from 0-2. It starts to show you a little bit about what we can do, but we have to find a way to close out the games."
Walker appeared to make it 1-0 at 15:40 of the first period, but the call on the ice was ruled no goal because of goalie interference. Kings coach Willie Desjardins challenged the play, but the call was upheld after a video review.
Doughty scored on a power play 22 seconds into the second period to give Los Angeles a 1-0 lead. His shot from the right point went in short side after deflecting off the stick of Avalanche forward Gabriel Bourque.
Walker extended the lead to 2-0 at 12:58 on a wraparound at the left post.
"You want to get your first one out of the way," Walker said. "I got the puck on the first goal and when they disallowed it, I threw that puck into the crowd. I have the one that counted."
MacKinnon scored 32 seconds into the third period to cut it to 2-1, driving to the net before redirecting a pass from Mikko Rantanen.
"We fought back and clawed our way back so hard, it's tough to swallow," Avalanche defenseman Erik Johnson said. "It was looking like we weren't going to come up with anything. We need these two points. We'll take the single one right now, but it certainly stinks not to get the extra one. I think it's time to wake up and take care of some of these wins."
