Logan Couture scored in regulation for the Sharks, who matched their longest winning streak of the season following a stretch of five losses in six games.
"Going in with a win was important," coach Todd McLellan said. "We're starting to feel a little bit better about ourselves again. It's something we want to maintain coming back on the 26th."
Richards scored the lone goal for the Kings, who had won their previous two games in a shootout. But Dustin Brown, who had the winners in those two contests, was stopped by Niemi in the third round this time. Los Angeles has scored fewer than three goals in regulation for 14 straight games -- the longest such streak in franchise history.
"We had the opportunities but it went to a shootout and our scorers couldn't get one past their goalie," Brown said.
After neither team scored in the first three rounds of the shootout, Clowe beat Quick with a forehand to the glove side. Clowe decided to change things up after usually going to his backhand in previous shootout encounters with Quick.
The decision paid off as he scored for the second time in four career attempts against Quick.
"I felt pretty confident in the forehand move now because of the fact it's worked a couple of times this year," Clowe said. "He stopped me last year on my backhand so I figured I'd try this."
Niemi ended it when he stopped Brown. Niemi also made 28 saves before the shootout.
The Kings were playing their second game under new coach Darryl Sutter, who won his Los Angeles debut Thursday night 3-2 in a shootout against Anaheim.
"We played better as the game went on and we had a real good third period," Sutter said. "The effort was great, but what will stick out is not being able to bury one of our other chances."
The Sharks had most of the chances in a scoreless third period, when neither team was able to break a 1-all tie. Quick made 14 saves in the period, including a tough one early against Couture. The Kings also killed two penalties and escaped a dicey situation with less than 5 minutes to go when Drew Doughty just got his stick on Patrick Marleau's rebound attempt in front of an empty net, deflecting it wide.
The teams traded goals in the second period, with Couture striking first for San Jose and Richards getting the equalizer for Los Angeles on the power play with 1:08 left.
Couture got his 15th goal on a sharp one-timer from the faceoff circle off a feed from Clowe midway through the period.
San Jose was unable to maintain the lead as its porous penalty-killing unit once again failed in a key spot after a questionable interference call against Couture. The Sharks, who are tied for the second-worst penalty-kill percentage in the NHL, had killed 10 straight penalties before Richards struck for his 13th goal of the season.
Anze Kopitar won control of the puck along the boards with three Sharks in the area. He sent a pass cross-ice to Richards, who was alone in the faceoff circle and beat Niemi with a wrist shot. Richards has scored in back-to-back games after missing the previous eight with a concussion.
The teams combined for only 12 shots -- seven by Los Angeles -- during a scoreless first period that did include a few good scoring chances for each side.
After a bad line change by San Jose, Brad Richardson was all alone at the side of the net but couldn't get off a clean shot, allowing Niemi to make a pad save.
Benn Ferriero then couldn't get his stick on a pass from Joe Thornton on a 2-on-1 opportunity for San Jose later in the period. The Sharks had two good scoring chances on a late power play, but Quick stopped Joe Pavelski at the side of the net. Justin Braun then missed the net on a big slap shot in the final minute of the period.
Los Angeles was 4 for 56 over its past 15-plus games on the power play before Richards' goal. ... The Sharks recalled G Antero Niittymaki from his conditioning assignment with Worcester after he underwent hip surgery in September. San Jose will carry three goalies for the time being. Thomas Greiss served as the backup to Niemi against the Kings.