The Kings scored 15 goals while going 2-8-1 in their previous 11 games, scoring as many as three goals twice, each in losses.
"You score five goals on the road, you should win," Kings coach Darryl Sutter said.
"I thought we played well, but we were down two goals," Kopitar said. "At the end of the day, we got the two points. It wasn't the easiest two points, but we'll take it."
Kopitar scored a power-play goal at 3:13 of the third period to give the Kings their 5-4 lead. He batted the puck out of the air and inside the right post after Jeff Carter deflected a shot by Tyler Toffoli with Avalanche defenseman Nick Holden serving a boarding penalty.
"It just pops up," Avalanche goalie Jean-Sebastien Giguere said. "It was a little scrambly out there. Those goals, it goes over your head and there's nothing you can do. The positive note is that we had a chance in the third and we just weren't able to get it."
Holden was assessed the penalty 10 seconds after the Avalanche killed off an interference penalty taken by Cody McLeod with 25.8 seconds left in the second period.
"It was great, down by two," Kings defenseman Matt Greene said. "I don't think we can say we've done that a lot of times, especially coming out of the break there and being in a shootout like we were tonight. Obviously, we got to buckle down defensively, especially on the PK. For us to come out and put up six, it's huge for our team. When you're down by two, that's awesome."
"He was awesome. He was lights out," Greene said of Jones, who had lost four consecutive decisions after starting the season 8-0-0.
Jones made a stop against McGinn driving to the net shortly after Kopitar put the Kings ahead and he made a stick save against Landeskog in the slot with six minutes to play.
The Kings also killed off what turned into a 6-on-4 Avalanche power play that started with 3:24 remaining. Giguere eventually left the ice for an extra skater after Greene was penalized for kneeing McGinn.
"We were resilient. We had our chances in the third period and he made some great saves on Landy, a great save on Jamie," Avalanche coach Patrick Roy said of Jones. "We had some good chances to make it a 5-5 game."
Kopitar and Carter scored 2:04 apart late in the second to tie the game 4-4.
Kopitar scored at 16:49 after his wraparound attempt went to Justin Williams in the slot. Williams passed back to Kopitar for a tap inside the post.
Carter scored at 18:53 after Mike Richards carried the puck from the right corner to the faceoff circle. He shot the puck and Carter tipped it by Giguere, who was screened on the play.
"Those two quick ones at the end of the second were huge and we carried that momentum into the third," Kopitar said. "It's nice to start off the third with a PP. We felt good in the second period, too. Our PK wasn't as sharp as we want it to be, but you obviously have to give them credit."
Jarret Stoll tied the game 2-2 for the Kings 24 seconds into the second period when he drove to the net ahead of Avalanche defenseman Tyson Barrie to convert a pass from Dustin Brown, who retrieved the puck after shooting wide on a breakaway.
The Avalanche went ahead 4-2 on power-play goals by McGinn and Andre Benoit.
"We were up 4-2 and I thought we played a good game," Roy said. "I thought we did a lot of good things. The last maybe couple minutes in the second we made a few mistakes, but they did a good job. That was a great tip by Carter in front of the net. It was a great job bringing the puck in front. They competed like we did. I thought it was a great game."
O'Reilly and PA Parenteau scored goals 5:15 apart in the first period to give the Avalanche a 2-1 lead.
Kings defenseman Robyn Regehr opened the scoring at 5:48 with a shot from the left point. All three of Regehr's goals this season have come in the past three games.
O'Reilly shot the puck off the left post shortly after Regehr scored and he tied the game with a power-play goal at 11:17 with Regehr in the penalty box for cross-checking MacKinnon.
Holden was between the faceoff circles when he passed to O'Reilly skating through the goalmouth. O'Reilly lifted the puck over Jones' right arm for his 22nd goal, tying MacKinnon for the team lead.
|Robyn Regehr (3) ASST: Anze Kopitar (31), Tyler Toffoli (10)|
1 - 0 LAK
|PPG - Ryan O'Reilly (22) ASST: Nick Holden (9), Jamie McGinn (11)|
1 - 1 Tie
|Pierre-Alexandre Parenteau (11) ASST: Matt Duchene (32)|
2 - 1 COL
|Jarret Stoll (7) ASST: Dustin Brown (7), Dwight King (13)|
2 - 2 Tie
|PPG - Jamie McGinn (15) ASST: Ryan O'Reilly (21), Matt Duchene (33)|
3 - 2 COL
|PPG - Andre Benoit (3) ASST: Nathan MacKinnon (23), Paul Stastny (25)|
4 - 2 COL
|Anze Kopitar (18) ASST: Justin Williams (16), Slava Voynov (20)|
4 - 3 COL
|Jeff Carter (21) ASST: Mike Richards (30), Matt Greene (4)|
4 - 4 Tie
|PPG - Anze Kopitar (19) ASST: Jeff Carter (18), Tyler Toffoli (11)|
5 - 4 LAK
|EN - Justin Williams (15) ASST: Drew Doughty (23)|
6 - 4 LAK
|Robyn Regehr Cross checking against Nathan MacKinnon|
|Gabriel Landeskog Holding against Matt Greene|
|Justin Williams Hi-sticking against Nathan MacKinnon|
|Jeff Carter Holding against Matt Duchene|
|Dustin Brown Interference on goalkeeper against Jean-Sebastien Giguere|
|Cody McLeod Interference against Dwight King|
|Nick Holden Boarding against Mike Richards|
|Matt Greene Kneeing against Jamie McGinn|