LAFC (8-7-4, 28 points) overwhelmed the Galaxy with foray after foray into the Galaxy end, and had the benefit of a man advantage for most of the match. Eight of their 27 shots were on target compared to five shots and one on goal for the Galaxy, who chose not to put their biggest name, Javier "Chicharito" Hernandez, in the lineup or on the bench.
The Galaxy (5-10-3, 18 points) have lost seven of their last eight matches, fueling speculation that head coach Guillermo Barros Schelotto is in his last days in that position.
LAFC's Diego Rossi, back from quarantine from international duty earlier this month, hit the bar across the goal in the 11th minute. LAFC also missed another chance to score later in the first half after a penalty call was rescinded.
On that 22nd minute play, the Galaxy's Giancarlo Gonzalez brought down Rossi near the top of the box with a hard challenge. The referee ruled it a penalty, but upon video review the call was changed to a foul outside the box, and free kick for LAFC.
LAFC didn't score, but the Galaxy were forced to play with 10 men from the 25th minute on after Gonzalez was sent off for denying an obvious goal-scoring opportunity.
"I think the red card changed the game. Maybe they managed the ball a little more than us, but we were defending, we were doing well, we were attacking with [Cristian] Pavon and Yony Gonzalez or sometimes on the right with Julian [Araujo]. But the game was very even, and the card changed it because we needed to play with one less player," Barros Schelotto said.
The Galaxy survived a few LAFC chances until the 58th minute, when Musovski ran down a long ball from Rossi and chipped a shot into an open net.
Vela made a triumphant return from a knee injury his first appearance in a match in more than two months, coming on as a substitute in the 68th minute. Vela, the MLS Most Valuable Player last season, scored in the third minute of added time in the second half to seal LAFC's win.
"It means a lot to everybody that Carlos, not only gets back on the field after being out for a while, but then scores an excellent goal. It's been really good just to have him back in training," LAFC head coach Bob Bradley said. "We're excited to get him back every day and keep trying to push him and have him really finish the season in a great way."
LAFC remained firmly in fourth place in the Western Conference standings with the Galaxy in last place, 12th out of 12 clubs.