Stoll scored the deciding goal in the tiebreaker -- his ninth in 10 attempts this season and eighth in a row -- giving the Kings a 3-2 victory against the Phoenix Coyotes on Wednesday night.
Quick improved to 10-0 in shootouts after denying a bid by Lauri Korpikoski to extend it to a fourth round. The Kings were coming off a 6-1 loss at San Jose in which Quick gave up four goals on 16 shots and was pulled for only the third time in 58 starts this season.
"In the shootout, Jonathan Quick is outstanding," coach Terry Murray said. "He really gets his focus, and sometimes he amazes me how he comes out on the end of a day during a shootout situation. He had to make the stops for us to win, and he did."
Los Angeles concludes its regular-season schedule with a home-and-home set against the Anaheim Ducks, who tightened their grip on a playoff berth with a 6-2 victory against San Jose.
The Kings and Ducks have never been to the postseason in the same year since the NHL expanded to Anaheim in 1993-94. But if the Kings win both, they can lock up fourth place in the Western Conference and home-ice advantage in the first round.
"Yeah, it's huge, and we want it," Stoll said. "Our goal was obviously to make the playoffs. The home-ice is there for us and these last two games are a big test for us -- and getting our game to where we want it to be for playoffs. If we do that we'll probably have home-ice because of it."
Stoll also had a goal in the first period, Kyle Clifford had the tying goal late in the second and Quick made 33 saves. The victory was the Kings' 46th, tying the franchise record set in 1990-91 -- when they had 10 games end in ties -- and matched last season.
"It's a win that you want to have, and that's a hard game to win," Murray said. "The guys stepped up. It was a fun game to coach. We can take a deep breath and breathe out, but we got two big games ahead of us against Anaheim, who are playing well."
Closing the deal on the playoff berth wasn't easy for the streaky Kings, who have been muddling along without their two leading point producers. Anze Kopitar missed his fifth consecutive game because of a broken right ankle and Justin Williams was sidelined for the seventh game in a row with dislocated shoulder. Their status for the playoffs is unknown.
Both teams came in knowing that a victory would mathematically put them in the postseason. The Coyotes need one more point to secure their second straight postseason berth.
"This is when it's fun -- when the games are really important and everything's on the line," said Lee Stempniak, who scored his 19th goal of the season and seventh against the Kings. "That's when you want to be out there and playing your best. I think it's good to get into that mindset."
Taylor Pyatt also scored for Phoenix and Ilya Bryzgalov made 31 saves. Pyatt was one of three players who returned to the Coyotes, along with Korpikoski and All-Star defenseman Ed Jovanovski. Jovanovski played his first game since fracturing the orbital bone in his left eye Feb. 17.
"It's a big point. But when you come all the way out here, you want to find a way to get both of them," Phoenix captain Shane Doan said. "We've been close, we've been around it, but we just haven't found ways to win games."
Pyatt put Phoenix ahead 2-1 at 17:58 of the first period, slamming his 18th goal into a wide-open net after Stempniak's wrist shot from a sharp angle to the left of the net caromed off Quick's left leg and into the slot.
"It's great to have Taylor back," Stempniak said. "There's not many guys that have the stance and are as big as he is or as strong on the puck, so it's a huge asset to us."
- Stoll, who scored the only goal in the Kings' victory against Phoenix on March 3 at Staples Center, became the sixth Kings player this season with at least 20. It's first time they've had that many 20-goal scorers since 1992-93, the only time they made it to the Stanley Cup Finals.
- The Coyotes are the only team in the league without a 20-goal scorer. Doan has 19 along with Stempniak.
- Stoll's tripping penalty at 7:51 of the first ended a stretch of 127 minutes and 59 seconds in which the Kings didn't have to use their penalty-killing unit -- which entered the game with the second-best percentage in the league (85.8). Kings opponents have scored only two goals in their past 49 power plays.
- The Kings will go into the playoffs without anyone on the roster recording at least 80 points, the ninth time that has happened in club history.
- The Coyotes' regular-season schedule, which began in Prague with two games against Boston, will conclude this weekend with a home-and-home set against the Sharks.
- Brown hasn't scored a goal in his past eight games against Phoenix. The Coyotes were one of only two Western Conference opponents he failed to score a goal against this season. The other was the Stanley Cup champion Chicago Blackhawks.