"They followed eastbound on Vernon. And, when they got to the intersection, here at Broadway, they observed the collision," said Lieutenant John Romero, Los Angeles Police Department.
It is unknown whether or not he was involved in a police pursuit at the time of the crash.
The collision knocked the Thunderbird out of control and into a woman waiting at a bus stop, killing her.
Relatives have identified the woman as 39-year-old Juliana Fallecio.
Officers who pulled the suspect out of the car were treated for smoke inhalation.
Police arrested 42-year-old Agustin Geronimo of Los Angeles, the driver of the gray Impala.
Eyewitness News anchor David Ono was shooting a story just a few blocks away. He was the first reporter on the scene.
A woman, who spoke to Eyewitness News, was nearly hit as well.
"The car jumped the pole, the police come around the other car, and the car almost hit me," the woman said. "I had to swerve to keep the car from hitting me."
Witnesses say the pedestrian was knocked 50 feet from the point of impact.
"I just seen her flew, from the light ... from the bus stop," said a man who said he had just given the victim $5 to catch the bus to visit her husband. She told the young man her husband was in the hospital.