Defenseman Alec Martinez also scored for the Kings, who improved to 11-1-3 since Jan. 22 following a 2-10 slide -- but not without making life nervous for the sellout crowd of 18,118 at the Staples Center.
"We made it interesting at the end just through getting too casual, a little careless with some plays at critical times at the game," a relieved coach Terry Murray said. "You go into the third period with that kind of scenario you want to make sure you're able to lock it down. Good teams do. You don't get reckless or careless and start taking some penalties, especially the high sticking penalties. We have to clean that part of it up right away."
Despite the late scare, the Kings now have 74 points, fifth in the West and one in back of fourth-place Phoenix, which has played one more game.
The Avalanche had totaled only 14 shots before Kings defenseman Matt Greene was sent off for interference with 8:53 remaining. Stoll joined him in the penalty box 13 seconds later for hooking. Jones scored his first on a power play. The other came one second after Stoll left the box. Stastny scored when Stoll accidentally kicked his centering pass into the net.
"We definitely can't be taking penalties that late in the game," Doughty said. "You see what happens -- they almost caught up and took it to OT and that's not something we want to be doing. We've got to learn from it, but [we're] happy with the game."
Before through the first 50-plus minutes, the Kings did almost everything right.
Kopitar gave the Kings a 1-0 lead at 7:13 of the first period with his 20th goal, converting a rebound after newly acquired Brian Elliott stopped Brad Richardson's wraparound attempt.
The Kings had a chance to add to their lead in the second period during a two-man advantage, but Elliott kept them at bay until 9:50 when Martinez beat him through a screen with a long slap shot.
"Penalties didn't help our cause," Avs coach Joe Sacco said after his team lost for the 12th time in 13 games. "We're taking penalties because we're making some mental errors. We made it close and we hung around and stuck it out till the end, but we need to be better than that. We have to start games better to put ourselves in a position so that we're able to stay in the game for 60 minutes. Today we got behind and we started chasing the game after that."
Los Angeles came up empty during another two-man advantage late in the second, but the Kings cashed in on a power play just 1.1 seconds before intermission. Kopitar banked the puck off the boards back toward the right point, where Doughty took a one-timer that dribbled over the goal line after Elliott appeared to have the puck trapped between his pads.
"We just didn't play," Avs defenseman John-Michael Liles said. "Obviously they're a talented team, a big team, and they took it to us in our end for quite a bit of time. It's not so much about making plays but about getting it in, getting the forecheck and when you do that, when we have our legs going, that's when were effective. We most definitely weren't effective in the first two periods."
The Kings lost forward Marco Sturm to Washington on waivers before the game. Their next game is Monday night, a few hours after the trade deadline.
Murray said he knows of no impending deals.
"There have been zero conversations with (GM) Dean (Lombardi and I about any player that's out there," he said.
"I like our team. I like the way it is right now, we've got a great chemistry, and that's so important, to have that chemistry. You can put a lot of different people into the dressing room and if it doesn't work, boy, you're very frustrated as an organization…We've got a good group of guys that play hard for each other."
Material from team media and wire services was used in this report