Ray McCallum netted 27 points and DeMarcus Cousins added 20 points and 10 rebounds for the Kings, who have won two straight on the heels of a three-game slide.
Jordan Hill tallied 18 points and 15 boards for Los Angeles, which has dropped four of its last five, and Jodie Meeks scored 21 in the loss.
The Lakers trailed 94-81 with 7:55 left in the fourth before they used a 10-2 run to get back in it. Nick Young and Wes Johnson jumpstarted the surge with 3-pointrs and Meeks capped it with a layup to cut the deficit to 96-91.
Johnson's tip-in with 1:06 to go pulled LA within 105-102 and it got a stop at the other end after Travis Outlaw missed a jumper. Kent Bazemore, though, was unable to get his layup to drop.
McCallum then split a pair of foul shots, but Ben McLemore snatched the offensive rebound and Outlaw hit 1-of-2 with 17.4 ticks remaining to seal the outcome.
Earlier, the Kings led 24-23 after a quarter of play, 60-52 at the break and 87-76 after three.