Quick's giveaway goal helped the Avs trim a four-goal deficit to one.
Quick was about to pass the puck to his defensemen on his right and never saw Brian Willsie, who intercepted the puck and put it into the net for his first goal of the season to pull the Avs to 6-4.
"It would have been a pretty nice assist if the guy was on my team," Quick said. "Unfortunately, he wasn't. he made a nice play and nice shot. The team bounced back. They responded after they scored that fifth goal and they played great defensively. That kind of took a little bit of pressure off me."
After Cody McLeod's goal 90 seconds later pulled Colorado to 6-5, the Avs had numerous chances to tie, but Quick made several nice saves to preserve the win.
"It's a great game for a rookie goaltender to deal with what's going on: the emotion in the game, the opposing team jamming the net and whacking away at him," Kings coach Terry Murray said. "He'll grow from this."
The Avs pulled their goalie with a minute left to no avail. Ryan Smyth's shot in the waning seconds was wide of the net, and the Kings celebrated their first two-game winning streak since Dec. 11-13.
"We made a couple of bad mistakes. It was a little nervous, but I think we responded pretty well," said Alexander Frolov, who scored twice for Los Angeles.
"We saw we were capable of scoring tonight and everyone tried to put the puck on the net and make something happen," Frolov said. "We have to learn how to play when we lead in the third period."
The Kings chased struggling goalie Peter Budaj with a three-goal onslaught in the second period.
Frolov's power play goal broke a 1-1 tie after John-Michael Liles went to the penalty box for hooking in the opening minute of the second quarter.
Nineteen seconds later, Jack Johnson's one-timer made it 3-1. Then Dustin Brown picked up a loose puck in front of Budaj, skated behind the net and passed it to Jarret Stoll, who put it high over Budaj, who was scrambling back into position.
That was all for Budaj, who has lost five of his last six starts.
He was replaced by Andrew Raycroft, who surrendered two quick goals himself before Colorado mounted a comeback that fell just short.
The Avs, who had won all three of their games against the Kings this season, pulled to 4-2 on T.J. Hensick's power-play goal, but a minute later, the Kings had doubled their cushion. Frolov's second goal made it 5-2, followed 21 seconds later by Brown's score that made it 6-2.
The crazy period ended with Colorado's Chris Stewart scoring with 7.2 seconds left, pulling the Avs to 6-3.
Colorado was trying to sweep the Kings in a season series for the first time since the franchise moved to Denver in 1995-96, and it seemed to have the right man for the job in the goal in Budaj. He was 3-0 with a 2.27 goals-against average against the Kings this season. In eight career appearances against Los Angeles, Budaj was 6-1-1.
"It was a crazy game," Avs forward Wojtek Wolski said. "The puck just seemed to bounce for them early and they got a couple of goals really quickly and that kind of put us down. But we seemed to find a way to get back into it. We had so many chances there at the end that we probably should have put one in."
The teams exchanged power play goals in the first period. Kyle Calder tipped in Drew Doughty's shot from the point to put Los Angeles on top 1-0, and the Avs tied it 5 minutes later when Marek Svatos put the puck past Quick.
After the game, the Avs reassigned D Kyle Cumiskey and F Chris Durno to the Lake Erie Monsters of the AHL. ... D Adam Foote (triceps) didn't play against the Kings after participating in practice Tuesday. ... The Avs have won six of eight from Los Angeles. ... The Avalanche are in the midst of an eight-game homestand, the second-longest in franchise history.