Quick was perfect in goal when he needed to be, and Richards scored the lone goal in a six-round shutout to give the Kings a 3-2 victory over the Blackhawks on Sunday night.
Richards beat Ray Emery with a quick wrist shot after Emery stopped the Kings' first five shooters.
Quick stopped all six Chicago shooters after making 35 saves -- including Viktor Stalberg's third-period penalty shot -- through overtime.
"I got fortunate there (in the shootout). I had a couple of guys mishandle the puck," said Quick, who shut out the Blackhawks in their last two meetings. "We got two points, that's all it means. It doesn't matter how we do it as long as we get it."
Slava Voynov and Jeff Carter scored in regulation for Los Angeles, which ended a two-game losing streak. The Kings and Quick rebounded from a 4-3 loss in Detroit on Friday night when they gave up two goals in the final 4:02.
"He (Quick) brings out confidence in the whole team, the whole game, the way he plays," Carter said. "Especially, when you get down to a shootout, 1-on-1, he's going to be ready so it's pretty nice."
Quick gave up four goals on 15 shots against the Red Wings, and in his previous three starts had allowed 10 goals on 72 shots.
The goalie ran his scoreless string against Chicago to 175:59 before Marcus Kruger scored in the second period. In three previous games against the Blackhawks this season, Quick allowed two goals on 84 shots.
Patrick Kane also scored for Chicago, tying it at 2 at 7:36 of the third with his fifth goal in seven games.
"It was a hard-fought two points for us," Quick said. "It's exactly what we needed and what we came here to do."
The matchup against Chicago might have been just what Quick needed.
"He's struggling, he's your No. 1 goalie and he goes out and, in a lot of ways, wins you the game," Los Angeles coach Darryl Sutter said.
Emery stopped 27 shots through overtime in his fifth straight start and eighth straight appearance. Corey Crawford, who began the season as the Blackhawks' No. 1 goalie, hasn't played since being pulled after one period Feb. 29 against Toronto.
"We had a tough first 10 minutes, but I thought we did a great job of coming back from that and battling back," Emery said. "We tied it up, had a big third, gave ourselves a chance to win.
"You want the two points, but every point's important this time of the year. It's important that we came back from that, and important that we got a point."
The Kings dominated early, outshooting the Blackhawks 14-6 through the first half of the opening period. Voynov opened the scoring for Los Angeles just 1:17 in, completing a 4-on-1 break after the Blackhawks were trapped deep in the Kings' zone.
Alone in front of Emery, Voynov ripped in shot from the slot after taking a short feed from Justin Williams. Voynov scored easily after the lone Blackhawk back, defenseman Brent Seabrook, slid on the ice to try to break up the pass.
Quick stopped a close-in attempt by Marian Hossa 5 minutes into the second. Midway through the period, Dave Bolland hit the post with a shot after Quick dove forward and left most of the net open. Kruger finally broke through against Quick on a rebound with 7:23 left in the second to tie it.
Following a turnover at the Los Angeles blue line, Chicago's Stalberg outbattled the Kings' Matt Greene deep in the zone for a loose puck. He passed to Patrick Sharp, whose shot was blocked by Los Angeles defenseman Drew Doughty.
The puck popped out to Kruger, who fired in his ninth goal of the season with Quick down. Carter restored Los Angeles' lead at 2-1 just over 5 minutes later.
Quick made a diving point-blank glove save on Bolland's shot from the low edge of the right circle just over 3 minutes into the third.
Quick then came up with a pad save on Stalberg on a penalty shot at 6:28 of the second. Stalberg was awarded the attempt after being pulled down by Rob Scuderi on a breakaway.
Kane tied it at 2 at 7:36. Quick stopped Hossa when he plowed to the net from the right corner, but Kane jammed the rebound in between Quick's pads.
"I thought we worked ourselves back into the game with a good second period." Chicago coach Joel Quenneville said "I didn't like the goals we gave up tonight, but we had a real strong finish."
Emery made a point-blank save on Dustin Brown 1:30 into overtime.
Richards' shootout goal was only his second in six attempts this season, but both have been game-winners. ... Chicago C Jonathan Toews missed his 10th game because of an upper-body injury, believed to be a concussion. Toews has resumed skating without contact. Before Kruger scored Sunday, Toews was the last Blackhawk to score against Quick, with 3:22 remaining in the second period of Chicago's 2-1 win on Nov. 26. ... Chicago D Steve Montador missed his 16th game with an undisclosed upper-body injury, and D Sami Lepisto missed his second with a leg injury. ... Los Angeles completed a four-game trip, going 2-2. The Kings also finished a 10-game stretch where they played eight games on the road, going 5-4-1.