Authorities responded to the fire at the 170 block of E. 50th Street shortly after 11:30 a.m. Thirty firefighters were able to douse flames in nine minutes.
"In my backyard, I could see the billowing smoke," said neighbor Alytino Brown.
The mother was declared dead at the scene. Paramedics tried to save a 2-year-old boy, but he was pronounced dead at a hospital. The woman's 8-year-old son was at school when the fire broke out, and the woman's husband was at work.
The deaths raise the number of fire-related deaths in the city this year to 11.
"Our annual average for the city of Los Angeles is about 20, so this is an alarming rate," said LAFD Capt. Jaime Moore.
The cause of the fire is under investigation. Investigators say the garage had been converted to a living space and did not have a working smoke detector.
There were no working smoke detectors in the nine previous deaths either. Firefighters have been going door-to-door in the neighborhood to make sure all the residents had working smoke alarms. Officials say of the homes they checked, 80 percent did not have any working smoke detectors.
It is not yet known if the converted garage was licensed or up to code.