Homicide detectives spent 10 hours scouring the crime scene for evidence, lifting fingerprints off parked cars and interviewing neighbors.
Authorities say the incident happened at the couple's residence in the 9700 block of Beach Street. The victims heard a car alarm go off at about 11:10 p.m. Sunday and rushed outside.
They were confronted by two men with guns. The confrontation moved inside the apartment and ended with the husband, a man in his 50s, being shot twice in the chest. He was taken to a local hospital, where he died a short time later. His wife was shot in the elbow.
"At this point, it appears he may have been chased into the home. We don't have confirmation, but we do know the suspects did fire their weapons inside of the residence," said LAPD Sgt. Frank Preciado.
Police say the suspects and victims may have known each other. The incident was not believed to be gang-related.
A description of the suspects was not immediately available. Anyone with information is urged to call the police at (877) LAPD-24-7.