With overtime appearing to be a certainty, Jack Johnson took a shot from the right point that Sanford kicked away. Doughty wristed the rebound past Sanford just before the horn sounded.
Los Angeles has won two in a row and Columbus has lost six straight. The Blue Jackets have only 13 wins for the season in 51 games.
The Kings never trailed, taking their first lead midway through the opening period on a power-play tally by Justin Williams. Derek Dorsett tied it 1:09 into the second, but Dustin Penner's goal with 5:28 left in the period again put Los Angeles in front.
Colton Gillies scored for Columbus 4:52 into the third.
Jonathan Quick allowed two goals on 22 shots to get the win. Sanford made 30 saves.