L.A. pulled even with San Jose with 82 points. The Sharks own eighth place because they have a game in hand on the Kings.
But the Kings, who host the Sharks on Tuesday, are playing with swagger these days.
"It was a huge game that had a lot of meaning for us," Penner said. "We have teams ahead of us that just keep winning, so we've got to do the same thing. Against a team like Nashville, where it was 1-1 going into the third, it was time to separate the men from the boys. I think we grew a lot, overall, in this game, especially in the third period to come out like that. We got contributions from (a lot) of guys."
Penner finished off a great cross-ice pass from Trevor Lewis, who sprinted down the right side with Shea Weber defending and set up Penner for a tap-in at 8:04 of the third period, breaking a 1-1 tie.
"I think we all three almost passed out in the corner there, screaming so loud," Lewis said. "It was a lot of fun."
King, a late season call-up, took a pass from Carter and slipped behind the defense and scored five-hole at 13:02 on Pekka Rinne for his fourth goal this season. Clifford scored on a breakaway at 16:19 to make it 4-1.
Penner has mostly had a forgettable season. He has suffered knee, hand and back injuries and been a healthy scratch five times this season. Los Angeles coach Darryl Sutter has used him in a defensive role on the third line with Lewis and Jarret Stoll.
Penner's goal was his sixth of the season and his first since Feb.7. Clifford's last goal also came on Feb. 7.
"We talked about it," Penner joked. "We're roommates on the road, and we had agreed that we're going to score together in the same game."
On a serious note, Penner said he it was a personal breakthrough.
"I'm not even concerned about the month (that) I haven't scored – it's all year," he said. "Hopefully this is something that will help me on a subconscious level."
Nashville got a late goal from Mike Fisher but fell two points behind fourth-place Detroit thanks to an uncharacteristically sloppy third period.
"We turned the puck over in the neutral and we didn't stop on the puck," coach Barry Trotz said. "We put it in the middle and they beat us to the net. They dumped the puck in the neutral zone (and) we lost a battle. They ended up scoring on both those goals. That can't happen. Those are the details that can't happen, especially when it's 2-1."
Jonathan Bernier got a rare start in goal for L.A., presumably because of his 5-1-0 career record against Nashville going into Saturday, including a victory in November.
"We have their number now," said Bernier, who found out late Friday that was getting a start. "You always get those teams that you feel good (against). Obviously I feel great when I play against them.
"We didn't quit and that's the biggest thing. When you're going to the playoffs you have to find a way to bury teams and that's what we did tonight."
Bernier made a glove save on Martin Erat early in the second and helped kill off two early penalties. But Nashville's top-ranked power play unit broke through on Dustin Brown's second cross-checking penalty when Erat's slap shot made it through a screen by Patric Hornqvist at 13:43.
Hornqvist induced Brown into the penalty near L.A.'s bench.
But the Predators were unable to carry over that strong second period.
"In the second period we started to get the cycle going and start funnel pucks to the net," defenseman Kevin Klein said. "We had a lot more opportunities and got away from that in the third."
Anze Kopitar, who beat Anaheim's Jonas Hiller with a wicked wrist shot Friday, scored with another laser shot from the right circle that beat a partially screened Rinne at 7:53 of the first period for a 1-0 lead.
After criticism earlier in the season for a lack of production, Kopitar has 26 points in the last 30 games.
Klein returned to the lineup after he missed eight games with an upper-body injury. Center Paul Gaustad was scratched with an upper body injury.
Nashville is overall a better regular-season team than L.A. but the Kings appear to be a bad matchup. Los Angeles is 3-1-0 against the Predators in each of the past two seasons.
"They play tight defensively," Erat said. "It's very hard to play against them."