LAFC needed the late heroics from Vela despite a 29-3 advantage in shots, including a 9-2 advantage in shots on goal.
Vela's game-winner came off a long pass from Kim Moon-Hwan to the left side of the penalty area. Vela knocked down the pass with his chest and one-timed a shot with his left foot over the head of RSL goalkeeper David Ochoa and into the roof of the goal.
Vela, the 2019 MLS MVP, scored for just the second time in 10 games (eight starts) this season. LAFC has won three consecutive games for the first time since August 2019.
Before the goal, it appeared as if RSL would steal a point behind Ochoa's strong play. Ochoa made eight saves, including a diving stop of a Vela penalty shot in the 60th minute.
Aaron Herrera scored a goal for RSL, which lost for the second time to LAFC in their last three games after dropping a 1-0 home decision on July 3.
Rossi gave LAFC a 1-0 lead in the 10th minute after working a give-and-go with Jose Cifuentes. Rossi passed to his teammate before sprinting through the RSL defense, getting the ball back and scoring past Ochoa.
Herrera tied the game 1-1 in the 18th minute on a counter attack. LAFC was overloaded on the offensive end for a corner kick, when RSL broke free.
Everton Luiz delivered a pass to Herrera as he sprinted in front of the LAFC defense and scored past Romero. It was just the second game where Romero allowed a goal.