Nathan Horton scored in his 600th NHL game, Artem Anisimov had a goal and an assist and Ryan Johansen also scored for Columbus, with James Wisniewski picking up two assists. Sergei Bobrovsky moved to 8-0 in his past eight starts with 26 saves.
Jeff Carter, Dwight King and Robyn Regehr had goals for the Kings, who have lost three in a row. Mike Richards had two assists.
The Blue Jackets have been surging since getting Horton, who missed the first 40 games after shoulder surgery, and Bobrovsky, who sat out most of December with a strained groin, back on the ice.
They're 8-1-0 with Horton, a big free-agent signing last summer from Boston, in the lineup.
Down 2-1 after the first, the Kings tied it before the Blue Jackets scored twice in 89 seconds late in the second to take command.
Carter, booed loudly every time he touched the puck, received a nice pass on a 3 on 1 break from Richards and recorded his 20th goal at 8:39.
Carter, who played an unhappy 39 games with the Blue Jackets in 2011-12 before being dealt to the Kings for defenseman Jack Johnson and a first-round pick, has goals in his past four games.
Each team came close to picking up goals before Columbus erupted in the final 2 minutes of the second.
Umberger shadowed defenseman Drew Doughty and stole the puck from him along the short boards, then put up what appeared to be an innocent shot from a hard angle. But Martin Jones, making his first start since Jan. 2, struggled picking it up and the puck caromed off his glove and into the net with 1:45 left in the period.
The Blue Jackets still weren't done, however.
Anisimov won a puck battle in the neutral zone and then carried the puck down the left wing. On a rush, he sent a tape-to-tape lead pass to Horton who lifted the puck high for his third of the season with just 15.6 seconds left for a 4-2 lead.
The Blue Jackets had killed off three first-period penalties and escaped the first 20 minutes with a 2-1 lead after falling behind early.
The Kings scored at the 2:42 mark when Trevor Lewis' shot from the right dot went off Bobrovsky's right leg pad to King, who was charging the net through the high slot. He had an almost empty net for his 11th of the season.
Columbus pulled even on the power play, where it has been particularly effective of late -- scoring on 6 of its past 13 attempts with a man advantage.
After defenseman Jake Muzzin went to the box for tripping, the Blue Jackets tied it when Wisniewski's hard slap shot from the top of the left circle was redirected in the crease by Umberger at 12:47.
It was his 12th of the season and his 114th as a Blue Jacket, moving him past David Vyborny into sole possession of second place in franchise history behind Rick Nash (289).
Then, in the final minute of the period, Johansen took a seeing-eye stretch pass from rookie Ryan Murray and glided past a defenseman to go high with a forehand to beat Jones. It was Johansen's 19th goal of the season.
Notes: D Fedor Tyutin, who became the sixth player to appear in 400 games with the Blue Jackets, returned after missing two games with an undisclosed illness. ... Los Angeles was playing its fourth of a five-game road trip. ... The Blue Jackets broke the franchise mark of six consecutive wins set from March 24-April 3, 2006. ... The Kings came in with a 5-1-1 record against the Metropolitan Division and as the only team in the NHL allowing fewer than two goals a game.