The driver was pursued by police to Marion Road and then to Sir Donald Bradman Drive, according to SA Police.
She then made her way to Henley Beach Road where an innocent motorists car was side-swiped by the driver at the intersection of South Road and Henley Beach Road.
Police continued to pursue the car to Port Road and then into the city along North Terrace.
The driver led police to Hackney Road before making her way to The Parade at Norwood.
PolAir, the police helicopter, was by this time monitoring the car and tracked the driver to Kensington Road and then south along Fullarton Road.
She then drove along Wattle Street and into the backstreets of Unley. Fortunately for police the driver then chose Fairford Street, a dead end road.
Patrols were able to swoop on the driver, placing her under arrest.
The woman is currently in police custody and is expected to be charged later this evening.