Galaxy stretched its winning streak to four games with a 3-0 victory in the derby clash at Dignity Health Sports Park.
Cristian Pavon opened the scoring in the 51st minute, lobbing Pablo Sisniega after the LAFC goalkeeper was left stranded having come to attempt to collect an Emiliano Insua pass.
Just two minutes later and LAFC was dealt another blow, Mark-Anthony Kaye sent off for a rash challenge on Julian Araujo.
Galaxy capitalised on its numerical advantage as Sebastian Lletget tucked away a smart Pavon set-piece in the 73rd minute.
Lletget sealed the win 10 minutes later, his overhead kick from Rolf Feltscher's cross finding the corner.
Galaxy jumped into fourth in the Western Conference after a second straight El Trafico win.
Columbus sits five points clear atop the Eastern Conference after a 3-0 win over FC Cincinnati.
Crew needed until the second half to break the game open at MAPFRE Stadium in Ohio.
Pedro Santos opened the scoring in the 52nd minute before Gyasi Zardes's brace.
Zardes got on the end of a Santos cross before later scrambling in to see Columbus to a seventh win in 10 MLS games this season.
Philadelphia Union is second to Columbus and recorded a 3-0 win over New York Red Bulls.
Minnesota United scored four second-half goals in a 4-0 win over Real Salt Lake, New England Revolution edged Chicago Fire 2-1 and Portland Timbers recorded a 2-1 victory against Seattle Sounders.
Inter Miami's struggles continued with a 0-0 draw against Nashville as former Juventus and Paris Saint-Germain midfielder Blaise Matuidi made his debut, while DC United and New York City also drew 0-0.