The Avalanche, who swept the four-game season series, crept within two points of the Kings (66-64), who hold the eighth and final playoff position with a slew of teams in pursuit.
"Everybody knows it was a big game," Avalanche coach Joe Sacco said. "One of the things that we talked about was that we start on time, and we did. It was one of our better starts lately. It keeps us right in the thick of things."
The Avalanche chased Kings starting goalie Jonathan Quick with three goals on 11 shots in the first period and made it 4-0 on a second-period goal by Stastny, his team-high 16th of the season.
Varlamov turned aside 31 shots for his career-high 16th win, his third against the Kings, who on Tuesday turned a 3-0 lead against Phoenix into a 5-4 shootout loss and are winless (0-3-1) in their past four games.
"I thought Varly was outstanding," Sacco said. "He had a real solid game and when we had a few mistakes there, a couple of breakdowns, he was right there. He made some big saves for us, especially when it was 3-0. He made some saves to keep it at that score. He played real well. He was solid all night long."
Varlamov had gone 1-5-1 in his previous seven decisions, which included a 5-2 loss in Winnipeg on Monday when he faced 25 shots.
"I was trying to do my best," he said. "I didn't play that well last game. This game against L.A. was very important for us. I think I played well for the whole game. Honestly, the guys helped me out by clearing out rebounds. It was a tough game and it was against a very good team."
The loss was Quick's fourth in a row, though two of them were back-to-back 1-0 setbacks last week.
"It is not about practice," he said of the Kings' troubles. "It is about being prepared to play games. I don't think tonight we were prepared enough and didn't get ready enough. They seemed to care a little more than us, and that was the difference in the game."
But the game was decided in the first period when Olver, Stastny and Jay McClement scored in a little over 10 minutes against Quick.
Olver, playing in his third game after being summoned from the minors last week, opened the scoring at 7:04 with his second goal. David Jones pried the puck loose in the corner and passed to Olver in the left circle for a shot that seemed to surprise Quick.
Stastny stripped the puck from Kings forward Kyle Clifford behind the net and stuffed it past Quick's left pad at 13:04 for his first goal in five games.
"Just a quick wraparound," Stastny said.
It was McClement's turn at 17:22. Chuck Kobasew passed across to Ryan O'Reilly on a 3-on-2 rush and O'Reilly fired a shot from the left circle. McClement was skating to the net when he got his stick on the puck and deflected it in off the far post for his eighth goal, one more than he had in 80 games last season.
"Landy took a punishing hit and the puck came loose and I was fortunate to put it in," Stastny said. "From start to finish we played our game and didn't sit back after we got up 3-0. We just kept attacking. With big points at stake sometimes you sit back and play a little defensive, which we didn't."
Avalanche right wing Steve Downie, who was acquired Tuesday from Tampa Bay in exchange for Kyle Quincey, skated on a line with Landeskog and O’Reilly. He had one shot on goal, two hits and a minor penalty in 16:20 of ice time.
"He got in late last night, so it was a quick turnaround," Sacco said. "He does have a presence out there physically. He plays the game hard and he was energetic on the bench. He gave us some life tonight, no doubt."
The only sour note for the Avalanche was losing defenseman Erik Johnson to back spasms. He played 4:26 in the first period and didn't return.
Brown, meanwhile, was in a sour mood after the game.
"I think we had a wakeup call tonight," he said. "Our attitude as a team needs to change, and it needs to change quickly. We are in a tough spot in the playoff hunt and we just have to keep moving forward."
1 - 0 COL
2 - 0 COL
Deflected shot -
3 - 0 COL
Wrist shot -
4 - 0 COL
4 - 1 COL
Misconduct (10 min)
Misconduct (10 min)