Anze Kopitar had a four-goal outing for the Kings.
Gabriel Vilardi scored the other goal for Los Angeles.
Drew Doughty had a pair of assists.
Pheonix Copley turned aside 26 shots for the Kings, who moved to 34-20-8.
Josh Morrissey scored twice and added an assist while Kevin Stenlund also had a pair of goals for Winnipeg, who dropped their 4th straight game.
Kyle Connor had the other Jet goal.
Mark Scheifele had a pair of assists.
Connor Hellebuyck made 32 saves for the Jets, who dropped to 35-24-2.
Josh Morrisey got Winnipeg on the board first 15:52 into the first period when he followed his point shot to the net and hammered the puck past Copley after Mark Scheifele poked the disc into the crease.
Morrisey made it 2-0 1:45 later when he took a feed from Dylan DeMelo before moving in and stepping into a slap shot, beating Copley high glove side.
The goal was his 13th of the season.
Anze Kopitar got Los Angeles on the board with a power play marker 26 seconds into the second when he backed into open ice after winning a faceoff and one timed a Kevin Fiala feed past Hellebuyck to make it 2-1.
Kyle Connor restored the two-goal cushion at 6:08 when he scored from the left side board hash marks after snapping the disc past Copley, beating him high glove side to make it 3-1.
The goal was his 27th of the season.
Kopitar made it 3-2 at 9:14 when he re-directed an Alex Edler shot from the point past Hellebuyck.
Kopitar scored his third of the contest just under a minute and a half later when he went to the net after winning a faceoff in the Winnipeg end, taking time to tip a Drew Doughty shot past Hellebuyck.
The goal was his 23rd of the season.
Kevin Stenlund scored at the 12 minute mark when he worked his way out of the corner and beat Copley blocker side with a high wrister to end a 13-game goal scoring drought.
Jet newcomer Nino Niederreiter introduced himself to Winnipeg fans with 1:51 left in the second after he took Kings defenceman Sean Durzi heavily into the boards and ended up pairing off with Adrian Kempe in the ensuing fracas.
Niederreiter was acquired by the Jets in a trade with Nashville over the weekend.
He took the extra two minute penalty but that didn't matter after Stenlund broke free and fired his second goal of the period shorthanded just 17 seconds later at 18:26.
The goal was his 5th of the season.
Kopitar scored his 4th of the night 1:26 into the third when Gabriel Vilardi tied it up 15:54 into the 3rd when he broke in alone and snapped the disc past Hellebuyck high glove side to knot the game at 5.
The goal was his 19th of the season.
The game went into overtime.
There was no scoring in overtime and the game went to a shootout.
LA-Vilardi (miss), Kempe (score) WPG-Scheifele (miss), Connor (miss), Wheeler (miss) SHOTS-LOS ANGELES 37 WINNIPEG 31
NOTES-Jets Centre Adam Lowry played in his 600th career NHL game on the night.
Los Angeles hosts Montreal Thursday while Winnipeg travels to Edmonton to face the Oilers on Friday.