Jonathan Quick made 36 saves in his 52nd career shutout for the Kings, while Frederik Andersen made 30 saves in his 19th career shutout for the Leafs. The Maple Leafs were shut out for the first time all season, while the Kings were shut out for the sixth time this season.
''Quickie was exceptional again,'' Los Angeles coach Todd McLellan said. ''It was a night where we played the type of game we probably had to play to win.''
The combination of defensive brilliance and offensive ineptitude continued in the shootout: Michael Amadio had a largely open net in the second round but shot it into Andersen's pad - and then Auston Matthews whiffed on the puck on the other end.
Kopitar finally became the first person to put the puck in the net in the third round, but William Nylander matched him. After Kempe scored, Mitch Marner lost control of the puck to seal it for Los Angeles.
''That was a pretty even hockey game,'' Toronto coach Sheldon Keefe said. ''Both goaltenders did a good job. ... It wasn't our greatest game or greatest effort by any means, but there's a team on the other side that did a good job as well.''
The Kings opened a nine-game homestand by extending the longest winning streak of their last-place season. They have won seven of their last 10 games, yet still have the Western Conference's fewest points and the NHL's second-fewest (58).
Toronto has lost on the first two stops of its three-game California road trip.
After three periods of scoreless regulation featuring 53 shots but few premium scoring chances, John Tavares took a hooking penalty 31 seconds into overtime, but Andersen was solid in net.
''It was great to play behind a team like that, that really made plays for me,'' Andersen said. ''(Quick) played incredible down there, too, so I don't think that's on the offense. That's one of best in the league when he's on his game. He pulled out some great saves when we had the chances.''
Nylander then got a breakaway with 1:13 to play, but Quick made a beautiful pad save that prompted Nylander to break his stick on the post in frustration.
Kasperi Kapanen's first-period breakaway shot off the post was likely the best scoring chance in the first 60 minutes. Both teams had solid chances in the third, but Quick and Andersen remained impenetrable.
The game was a homecoming for Leafs forward Kyle Clifford, defenseman Jake Muzzin and goalie Jack Campbell. All three were Kings regulars who made their first returns to Staples Center since getting traded to Toronto over the last 14 months.
Clifford won two Stanley Cup titles while spending the past decade as a dependable two-way forward for the Kings, who drafted him in 2009. Los Angeles traded him to the Leafs on Feb. 5 in a deal including Campbell, the once-underachieving goalie who played his way into an NHL career with the Kings over the past two seasons.
''This place is special,'' Campbell said.
Muzzin was traded to Toronto in January 2019 after nine years with the Kings, who signed him in 2010. Muzzin and Clifford both weren't yet Kings regulars during the club's first Stanley Cup run in 2012 but both were dependable regulars during Los Angeles' second championship season in 2014.
Clifford and Campbell both waved at the LA crowd in response to loud cheers when they were shown on the scoreboard. Muzzin sat out his fourth straight game for Toronto since breaking his hand late last month, and he acknowledged the roars with a wave from the press box.
Trevor Moore also started at center for the Kings in his first chance to play against Toronto. Moore played 52 games for the Leafs over the past two seasons before the Kings acquired the LA-area native in the trade for Clifford and Campbell.
NOTES: Kings F Jeff Carter missed his seventh straight game with a lower-body injury. The team doesn't know when the veteran goal-scorer will return. ... Moore signed with Toronto as an undrafted free agent in 2016 and won the Calder Cup with the AHL's Marlies in 2018. ... Toronto D Rasmus Sandin returned to the lineup after a one-game absence as a healthy scratch. The teenager turns 20 years old on Saturday.
Maple Leafs: Visit the Anaheim Ducks on Friday night.
Kings: Host the Minnesota Wild on Saturday.
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