Firefighters responded to the crash in the 3900 block of South Buckingham Road just after 1:20 a.m., according to the Los Angeles Fire Department.
A natural gas line was severed in the crash, but a fire was not ignited, officials said.
The car slammed into a bedroom in the home, trapping an elderly couple inside. Two Los Angeles police officers suffered minor injuries in their attempt to rescue them but declined to be taken to a hospital.
A woman who lives in that house with her parents told Eyewitness News she didn't even hear sirens, just the car slamming into the home. Paulina Zamudio said she found her father trapped but could not find her mother at first.
She said the couple had just celebrated their 66th wedding anniversary.
"She was a very loving person who cared about other people," said Zamudio about her mother. "She taught us to care about people, whoever they were. It's a great loss to us, but everyone else who knew her also will miss her."
The woman, identified by police as Aida Villavicencio, was pronounced dead at the scene. The 92-year-old man was extricated and taken to the hospital with head trauma in critical condition, according to the Los Angeles Police Department. Family says he is physically OK.
Police say the pursuit started when the chase suspect, 26-year-old Eliseo Ixchopcalel, rear-ended a patrol vehicle at Hobart and Martin Luther King Boulevard. When officers began to approach the vehicle, he fled and led police on a pursuit.
Ixchopcalel was arrested and taken to the hospital in stable condition. He was booked for vehicular manslaughter.