Marcus Kruger scored the tiebreaking goal on a double deflection in the second period for the defending Stanley Cup champions, who had lost five of six.
Bryan Bickell also scored and Corey Crawford made 31 saves as Chicago swept the three-game season series between last season's Western Conference finalists.
Anze Kopitar had a goal and two assists in Los Angeles' highest-scoring performance since Jan. 21. Drew Doughty and Tyler Toffoli also scored, and Jonathan Quick stopped 25 shots in the Kings' ninth loss in 10 games.
With Chicago's victory and Anaheim's loss to Columbus, the Blackhawks pulled within three points of the Ducks for the overall NHL lead.
Kane warmed up for the U.S. Olympic team with his first multigoal game since Dec. 14, while Canadian Olympic counterparts Patrick Sharp and captain Jonathan Toews picked up two assists apiece. Leddy contributed his first goal and first multipoint game since Dec. 23.
Although the Kings scored more than one goal for the first time in seven games, it wasn't enough to beat the NHL's highest-scoring team, which had lost two of three on its six-game road trip heading into the Olympic break. Los Angeles had scored just three total goals in the last six games heading into this meeting of the NHL's last two champs.
The Kings got off to a horrific start yet again: Doughty took a charging penalty 24 seconds after the opening faceoff, and Kane walked in on Quick alone from the corner and beat his U.S. Olympic teammate for his 26th goal 1:02 in.
After Bickell scored on a pass from Kane, Doughty kept it close with his eighth goal on a one-timer moments later. His goal was the first by any Kings player except Kopitar in nearly two weeks.
The Kings shook their malaise between the first two periods, putting 11 shots on Crawford's net in the first 7 1/2 minutes of the second and briefly taking control of the game. Kopitar evened it with a flip of a bouncing puck on a 3-on-1 rush, taking a pass from Carter for his 17th goal.
But Chicago went back ahead on a circus goal. Leddy's shot from the point deflected off Kruger's blade and then smacked into Kings defenseman Matt Greene's stick in front of Quick, popping over the goalie's shoulder for Kruger's sixth goal.
Leddy then scored off the post on a long slap shot with 12:59 to play, and Sharp stole the puck from Willie Mitchell to set up Kane's second goal moments later.
Toffoli scored his 10th of the season—and first since Dec. 19—late in the third.
NOTES: Quick has started 15 of the Kings' 16 games since he returned from a seven-week injury absence. ... Bickell sat out three of the Blackhawks' last four games during a prolonged slump for the forward, who had just one goal in his previous 15 games. ... Chicago scratched Slovak Olympian Michal Handzus, who hasn't scored a goal since Dec. 27. ... The Kings scratched F Jordan Nolan, and Matt Frattin returned to the lineup after sitting out the past four games.