William Eklund and Justin Bailey also scored in regulation for the NHL-worst Sharks, who earned their first road win against a Western Conference opponent this season and won their second consecutive game overall.
They have not won three straight all season and will get their fourth chance to do so Tuesday night when they host the New York Rangers.
“It’s fun to win, especially back-to-backs, and I think we played a really solid game at both ends,” Zetterlund said. “We’ve just got to stick to it tomorrow.”
Logan Couture and Zetterlund converted in the shootout. Kaapo Kahkonen made 44 saves and denied both Los Angeles attempts in the tiebreaker.
Drew Doughty, Trevor Moore and Quinton Byfield scored for the Kings, who have lost 11 of 13. David Rittich stopped 24 shots. Byfield also had an assist, and Kevin Fiala had two assists.
“I wouldn’t say the season’s slipping away, but I would say there is concern and there is some frustration, definitely frustration” Kings coach Todd McLellan said. “We’re chasing it both ways. We tried to fix the offense and there’s something going wrong with the defense, and vice versa.”
Doughty salvaged a point for Los Angeles by burying a power-play slap shot during a six-on-four advantage with 1:58 remaining in the third period to tie it 3-3. But after neither team was able to score in overtime, Kahkonen turned aside Moore and Adrian Kempe in the shootout before Zetterlund ended it.
“Unfortunate the way the third goal went in for them, and we survived overtime,” Sharks coach David Quinn said. “Just a real gutsy win coming in here, playing the way we did.”
The Sharks went up 2-0 midway through the second on goals from Zetterlund and Eklund before Moore got the Kings on the board late in the period.
Zetterlund got his second goal and third point in two games during a delayed penalty, and Eklund ended a prolonged scoring drought with his first tally since Dec. 12 when he finished off the rush.
“We just kind of changed our mindset a little bit and took advantage of being structured and competing,” Quinn said.
Moore gave the Kings a much-needed spark when he chased down Fiala’s entry pass with speed before beating Kahkonen at the far post.
Byfield tied it 2-2 early in the second, notching his fourth goal in six games by finishing off Kempe’s pass after being returned to the top line with Kempe and Anze Kopitar.
“I thought they needed a little more energy, and naturally Q’s been there before and done that for that line, so that’s why that change was made,” McLellan said.
Bailey scored on a breakaway at 6:17 to put the Sharks back in front before Doughty struck late.
“Good comeback, obviously tied it up late,” Kempe said. “Still frustrating that we can’t be as efficient as we want and score on the chances we get.”
Sharks defenseman Mario Ferraro did not return after he was hurt on a hit into the boards by Kings center Trevor Lewis late in the second. Ferraro tried to take a warmup lap before the start of the third but immediately went back to the dressing room. Quinn expects Ferraro will miss games.
Kings defenseman Matt Roy was a late scratch after his wife gave birth to the couple’s first child earlier on Monday.
Up next for Kings: vs. the Buffalo Sabres at Crypto.com Arena on Wednesday night.