The collision was reported about 4:19 a.m. in the 1000 block of 7th Street, according to fire officials. The vehicle drove onto a sidewalk where the victims were sleeping, struck the woman and pinned the man, Los Angeles police said.
Firefighter-paramedics responded to the scene and found the man pinned under the four-door sedan.
News video showed a good Samaritan and seven firefighters lifting the vehicle with their bare hands while two other firefighters pulled the victim to safety.
Police said the man was in critical condition with a collapsed lung and back injury, and the woman suffered minor injuries.
Authorities from the LAPD said the driver, a man in his 20s, was arrested at the scene for felony DUI involving narcotics. Police said they found prescription medication in the vehicle, and the driver admitted to being "cracked out."