Vela's second goal came from the penalty spot in the 68th minute to give his team a second lead. Two minutes later his corner found Ryan Hollingshead for the eventual game-winner as LAFC (5-0-2, 17 points) remained the only unbeaten team in MLS.
Vela, LAFC's first signing before their introduction to MLS in 2018, now has 10 goals and three assists in 10 all-time MLS appearances against the Galaxy. This was LAFC's first win in the rivalry as the road team.
John McCarthy made three saves, including an exceptional late one-vs.-one stop on Javier "Chicharito" Hernandez, to help LAFC earn a fourth straight win in all competitions. Two of those have come in MLS play and the other two came in a 6-0 aggregate victory over the Vancouver Whitecaps in the CONCACAF Champions League quarterfinals.
Chicharito assisted Marky Delgado's late goal in his first start of 2023. But that couldn't prevent a third consecutive defeat for the Galaxy (0-4-3, 3 points), a slide during which they've conceded eight goals.
After a lethargic start to the second half, the game came to life when Jose Cifuentes reacted to steal a sloppy Galaxy throw-in.
Two minutes later, Hollingshead made it 3-1 when he evaded Delgado to reach Vela's in-swinging corner and head past Klinsmann from close range.
The Galaxy pressed ahead and might have come all the way back with better luck. Riqui Puig struck the left upright on a shot from distance moments before Chicharito was denied on the break by McCarthy in the 82nd minute.
Delgado closed it to within 3-2 when he tapped in Chicharito's cross from close range in the 84th minute, but McCarthy made another save of Lucas Calegariin stoppage time as LAFC held on.
The rivals were supposed to meet in their season openers Feb. 25 at the Rose Bowl, but a heavy rainstorm forced postponement of that matchup to July 4.
Giorgio Chiellini wasn't in uniform for LAFC due to a leg injury that hadn't been disclosed during the club's week of training.