That leaves the New York Rangers with little hope of making much of a series out of the Stanley Cup finals.
Quick stopped 32 shots in his best start of the series, Jeff Carter scored in the final second of the first period, Jake Muzzin and Mike Richards added goals in the second, and the Kings beat the Rangers 3-0 on Monday night to move within one win of their second Stanley Cup title in three years.
Los Angeles leads 3-0 and can claim the Cup on Wednesday night in New York. The Kings have already survived three Game 7s on the road, so this amount of success has their confidence soaring.
Quick hardly showed it when he took the podium wearing a black hooded sweatshirt.
"I don't think it would be any different if we were down 3-0," Quick said. "We're just trying to win a game in a couple days here. That's the focus."
After the Rangers blew two-goal leads in each of the first two games of the championship round in Los Angeles, they came home and couldn't get anything going against Quick.
The All-Star was sharp early and in the middle when the Kings built their lead. Not even six power plays could jump-start New York's offense.
"We did a lot of things the right way," Quick said. "Now we get ready for the next one. The fourth one is always the most difficult."
Los Angeles escaped with two overtime wins at home and then took complete command inside Madison Square Garden.
The Kings grabbed their first lead of the series on Carter's goal and then stretched the edge to three goals in the second -- something the Rangers failed to do in California.
While there has been only one comeback from a 3-0 hole in the finals, the Kings erased such a deficit in the first round against San Jose.
"Well, we know it's possible," Richards said. "The last game is always the hardest. We played a good game. We're going to have to play a better game if we're going to want to have success."
New York's Henrik Lundqvist was hardly at fault on the goals and finished with 12 saves. He was just outdone by Quick, who was perfect at the other end of the ice.
"You try to stay positive right now, but it's tough. It's really tough," Lundqvist said. "We are doing a lot of good things, but you look at the goals, and we put two in our own net. Then just a tough play on the third one."
Quick, a Connecticut native who grew up a fan of the Rangers and 1994 Stanley Cup-winning goalie Mike Richter, made a brilliant save with his stick blade to deny Derick Brassard shortly after a Rangers power play. That stop came on the heels of Brassard having two chances during the advantage off a rebound of Brad Richards' shot.
Brassard's first attempt was blocked, and the second was stopped by Quick.
The Kings goalie also was on his toes just 8 seconds into the third when Chris Kreider came in alone but was stopped in tight. That eliminated the optimism the sold-out, towel-waving crowd had for a big comeback.
"You've got to finish in this game. It's a performance-oriented business," Rangers coach Alain Vigneault said.
Los Angeles took its first regulation lead in the series when Carter scored his 10th of the playoffs on the Kings' fifth shot. Carter snapped a hard drive that clipped the skate of diving defenseman Dan Girardi in front and caromed inside the right post with 0.7 seconds left.
The red and green lights behind Lundqvist both flashed while the Kings celebrated. At no point did they hold the lead at home in the first two games until they ended each contest with an overtime goal.
"It was an unfortunate goal to give up at the end of the period," Rangers defenseman Ryan McDonagh said. "I thought our guys stayed with it and tried to come out with some energy, and created a lot. It was a tough one."
The quick pace played into the Rangers' preferred style, but New York managed only four shots in the first period. The Rangers led 2-0 in each of the first two games but couldn't hold on. They nearly took the lead again when Mats Zuccarello faced an empty net at the left post, yet he was stopped by Quick's lunging stick.
The Rangers' early 2-0 lead in the series opener became a 3-2 loss when Justin Williams scored in overtime. They held three two-goal leads in Game 2, only to be thwarted when Kings captain Dustin Brown won it in double overtime Saturday.
Quick had plenty of support in front of him to post his second shutout in these playoffs and ninth overall in the postseason.
"The team played great in front of me, cleared out a lot of rebounds that I left in front," Quick said.
Muzzin made it 2-0 at 4:17 of the second after former Rangers forward Marian Gaborik and Anze Kopitar worked the puck up the right wing wall to Muzzin at the point for a shot that struck New York's Martin St. Louis and found its way past Lundqvist.
Mike Richards finished a 2-on-1 with Trevor Lewis when his attempted pass across bounced back to him off McDonagh and was put it with 2:46 left in the second.
Gaborik played his first game at the Garden since being traded by the Rangers in 2013. ... The Rangers are 3-for-44 on the power play at home in the playoffs. Los Angeles went 1-for-4.