The accident happened Saturday afternoon in front of the Gompers housing complex in East St. Louis, the St. Louis Post-Dispatch reported.
Police said one of the two boys, who are 11 and 12 years old, had taken their mother's keys without her knowledge and accidentally shifted the car into drive as the boys were playing. The car rolled forward and over 15-month-old Jay'lah Keith, who was standing in a nearby yard.
The boys jumped out of the car to try and help Jay'lah as the car rolled across the street and into a telephone poll.
"They panicked," said family friend Sherwin Haywood, 56, who lives in the housing complex. "They didn't know what to do."
Jay'lah's grandmother, Elverita Graham, 56, said the girl's father, Marseani Keith, 23, took her inside to get her help and to call 911. Jay'lah was pronounced dead later.
The boys were questioned by police but Police Chief Michael Floore called the incident an accident.
Graham said she doesn't blame the boys.
"It was an accident and I don't want to see them punished," Graham said. "They're young and they've got their whole lives ahead of them. I know they didn't mean to do it. It's just a horrible situation for everybody."
At a candlelight vigil Sunday night for Jay'lah, her mother, Whitney Cole, 24, urged parents to keep an eye on their children.
"This is an eye-opener," she said. "Watch the babies, we don't know what they'll do until it happens."