The toddler's mother, Kimberly Black, 29, of Cleveland, was found naked several blocks away and was arrested.
The death of Sharice Swain, 29, of Cleveland, was being investigated as a homicide. Police identified the other victim as 2-year-old Kimshia Ruffin. Her 1-year-old sister, Taraji Ruffin, also was struck, but her injuries were not considering life-threatening.
The violence began Thursday night when Black and Swain were sitting in a running car parked in Black's driveway and got into an argument, police said. Black left the vehicle, went into her house, returned with a knife and stabbed Swain in the face and neck, police said.
According to Sgt. Sammy Morris, a police spokesman, the injured Swain then stepped on the gas pedal and hit the two young children, who were standing near the car. The car also struck a house, collapsing the roof of the porch.
The nature of the argument involving Black and Swain wasn't disclosed, and it wasn't clear if Swain hit the children intentionally or accidentally.
The women had been "best friends since birth" and Swain considered Black a cousin, according to the victim's mother, Anita Swain.
Anita Swain said her daughter did not have any children and was employed as a factory worker. She said she didn't know what started the argument and declined to comment further.
Nikki Randall, 30, whose daughter goes to school with Black's 6-year-old daughter, said neighbors who went to the aid of Sharice Swain after she was stabbed think Black was the intended target of the revving vehicle.
"It was on purpose," Randall said. "She was actually trying to hit the momma."
According to Randall, the naked Black was holding her two injured toddlers after they were struck and dropped Kimshia. Randall said she picked up the bloodied Kimshia and cradled her in her arms until firefighters arrived and took over.
"She was bleeding out of everywhere," Randall said. "As soon as I handed her to the paramedic, she went limp."
Black apparently had taken off her clothes after the stabbing and fled, authorities said. Upon being taken into custody, she was treated for a hand injury at MetroHealth Medical Center, then was arrested and locked up pending possible charges.
According to court records, Swain pleaded guilty to aggravated assault in 2005 and to permitting drug abuse in 2007. Both times she was placed on probation.
Down the block from the stabbing, Julius Jackson shook his head in disbelief Friday over the attack and subsequent car crash as he watered his newly planted vegetable garden.
"Oh, man, it's shocking to me," said Jackson, who said he keeps to himself in a neighborhood where people frequently move in and out.
Black's arrest occurred a half-block away from the location of the now-demolished house where the remains of 11 murdered women were found in 2009. The killer, Anthony Sowell, is appealing his murder conviction and death sentence.
Associated Press Writer Ann Sanner in Columbus contributed to this report.