The driver who crashed into The Rock's mother and cousin earlier this month was evading police and ran a red light just before the crash ... TMZ has learned.

As TMZ previously reported, Ata Maivia-Johnson (Rock's mom) and Lina Fanene (cousin) were driving home from a charity event in Clermont, FL August 2 when they were involved in a head-on car accident.

The Lake County Sheriff's Department tells TMZ ... an officer was attempting a traffic stop when the driver took off and ran the light. Sheriffs say the officer began following the driver ... minutes later the woman crashed into the car with The Rock's family.

The female driver suffered facial injuries and was taken to the hospital. The Rock's mother and cousin were also hospitalized with injuries.