Oakland police say that the young boys were driving a white Toyota sedan when they sideswiped a car heading the other way and hit the woman walking her dog. The car then crashed into a retaining wall.
It happened around 9:35 a.m. Thursday at 35th Avenue and Mangels Avenue, not far from Interstate 580.
The boys' uncle said that they took their parents' keys while they were sleeping. They live several blocks away from where the crash happened.
The woman and both boys were taken to separate hospitals. Police say that the woman is in critical condition.
According to the boys' uncle, the 7-year-old has a broken leg and the 4-year-old has a concussion.
He says he does not know why they stole the car or how they were able to operate it.
Surveillance video obtained by ABC7 Eyewitness News shows the moment the white sedan moves into the oncoming lane, sideswiping the other car and bouncing off in the other direction. At the same time, the woman walking her dog is in the crosswalk of an adjacent street as the car heads straight toward her.