The Kings (32-21-13), who are 3-0-1 in their past four games, are one point behind the Winnipeg Jets for the second wild card into the Stanley Cup Playoffs from the Western Conference. The Jets, who lost 5-4 to the St. Louis Blues, have 15 games left, and the Kings 16.
"Playing playoff hockey right now," McNabb said. "We're in a dog fight. We have to bring it every game. It's more urgent. We need to get points. It's a little playoff series between (the teams in the) eight, nine and 10 spots. Something we've got to continue."
The Avalanche (30-26-11) had won three games in a row to match their longest winning streak of the season. They are seven points behind the Jets with 15 games remaining.
Kings goalie Jonathan Quick made 21 saves for his 28th win.
Pickard was recalled Monday from the Lake Erie Monsters of the American Hockey League because Semyon Varlamov is out with a groin injury.
"It was a tough start for me," Pickard said. "I had a few saves at the start, the deflection goes in, and I'm not into a great rhythm. They earned a couple of those goals, but I have to find a way to make at least one, maybe two more saves out of those three. The goals weren't bad goals, but I have to find a way. I wasn't getting many bounces going my way there early on and before I knew it there were three in the back of my net."
The Avalanche drew within 4-2 at 8:27 of the third period when Alex Tanguay scored into an open net off Marc-Andre Cliche's pass, but Jake Muzzin answered for the Kings at 9:56. Muzzin beat Berra from the top of the left circle for his seventh goal, first in 18 games.
Williams said the Kings seem to step up their play when they're in desperation mode.
"We're at our best when we're in dire need of a win, and we're in dire need of 16 more wins," he said. "We have to do what we have to do and start winning on the road because we have a lot of road games left."
The Kings grabbed an early 2-0 lead on goals by Marian Gaborik and Jeff Carter. Gaborik tipped in McNabb's shot on a power play at 7:47 of the first period to open the scoring and end the Avalanche's penalty-killing streak at 19 in a row.
The Avalanche cut the deficit to 2-1 at 12:53 on a goal by Tyson Barrie, his 11th. Gabriel Landeskog passed to Barrie, who skated down the left wing and cut to the near hash marks for a shot past a screened Quick.
Clifford got that one back for the Kings at 14:15 when he scored from the point for his second goal of the season.
Clifford increased the Kings' lead to 4-1 at 15:03 of the second period during a scramble in front of Berra, who finished with 20 saves. It was his fifth goal.
"This time of year, we've got to play our best hockey," Clifford said. "It's one game at a time and points are huge. It's playoff hockey. It's not always going to be pretty, you just have to go to the net and we did that tonight."
The Kings killed off two penalties in the second period and three for the game while limiting the Avalanche to one shot. They've killed 40 of 42 penalties in the past 16 games.
"They played well, I have to give them credit," Avalanche coach Patrick Roy said. "This is a team that won two Stanley Cups in the last three years. I would say this: They're healthier than us right now, and half of our team are watching the game on TV. When you play a team like this, it makes it even more of a difficult challenge.
"I'm disappointed that we lost, but our guys never gave up. As a coach, at times I have to draw a line where I'm looking at their lineup and I'm looking at our lineup. I would love to play them with a full lineup and see how we would play them."