Quick, who stopped two of three Washington attempts in the shootout, tied Rogie Vachon for the Los Angeles franchise record with his 171st win. Kings coach Darryl Sutter also earned his 500th career victory to tie Toe Blake for 17th in NHL history.
Quick downplayed the individual mark, and it wasn't lost on him that it was achieved in the modern era.
"To be honest, I didn't know I was that close until a couple of games ago and someone brought it up," he said. "It's special, and wins are a team effort, so I think that makes it a little more special and enjoyable because it's 20 guys contributing towards wins. Obviously, if it wasn't for the shootout, [I'd] be another season behind. He didn't have the luxury of the shootout. In my mind, [I'm] still chasing him."
Sutter isn't one for individual acknowledgments, but he did say the milestone victory meant "a lot" to him.
"I've been around a long time. Kind of odd in the shootout though," he said.
Washington saw its three-game winning streak end despite a late rally. The Capitals tied it 1-1 with 7:36 left in regulation when Joel Ward chipped in the puck from the slot to reward great stickhandling in the corner by rookie Evgeny Kuznetsov. It was Ward's 22nd goal.
The Capitals nearly pulled off a rare feat by getting a win after erasing a third-period lead for the Kings, who were coming off three straight one-goal losses; the most-recent defeat, a 4-3 loss to the Phoenix Coyotes, marked the first time this season they lost when leading after two periods.
Washington's top-ranked power play went 0-for-3, including a 4-on-3 opportunity in overtime in which the NHL's leading goal-scorer, Alex Ovechkin, flubbed a shot from the left side.
Ovechkin has not scored a goal in five career games at Staples Center.
"Great chances there," Capitals defenseman Mike Green said. "[Chris] Brown in front all alone, and the puck bounces back out over to [Ovechkin], and he just didn't get a great shot off. That's the difference in the game there."
Quick allowed some soft goals Monday in the loss to the Coyotes, but looked particularly sharp in the second period with consecutive point-blank saves on former Kings forward Dustin Penner, the second with the cuff of his glove. He also stopped a between-the-legs shot by Troy Brouwer and poke-checked Ovechkin on a backhand try to preserve a 1-0 lead.
In overtime, Quick got a leg on Brouwer's attempt on the doorstop during a Capitals power play. Quick stopped Ovechkin and Nicklas Backstrom in the shootout after Kuznetsov had scored on the Capitals' first attempt.
Quick has allowed four or more goals five times this season, and in his subsequent games he has allowed three, one, zero, one and one goals.
"That's who they are," Capitals coach Adam Oates said of the Kings. "The goalie played great. The goalie maybe stole it for them, but they play a hard-nosed, physical game, and they did, and I'm proud of the guys, the way they stood up to it. You know, the second half of the game, I thought we kind of took it to them. We had a lot of good chances. I would say we carried the pace a little bit."
The Capitals, who have struggled to put the puck on net early in games, had eight shots halfway through the game before a late second-period push got them up to 13 shots at the second intermission.
"I think it took us a little while to feel them out," Green said. "Once we did, we kind of tried to expose some of their weaknesses. The forwards did a great job of that. Their goalie made some great saves, Quick, and kept them in the game. All around, I felt it was a good game."
Washington never trailed during its winning streak, but Gaborik showed some chemistry with Anze Kopitar on a late first-period goal that gave Los Angeles a 1-0 lead. Gaborik beat John Carlson to negate an icing call and fed Kopitar for a shot that went under Capitals goalie Jaroslav Halak from the left side at 14:09.
It was Kopitar's 22nd goal. Gaborik has at least one point in three of his past four games.
Halak finished with 27 saves in regulation and overtime before allowing two goals in the shootout. Jeff Carter scored the other Los Angeles goal in the tiebreaker.
Kings captain Dustin Brown returned from a lower-body injury and played with considerable energy on the third and fourth lines. He also saw time on both special-teams units.
The Capitals haven't won at Staples Center since Dec. 14, 2005, and have lost six straight to the Kings.