The boy, 14, is being treated for a gash to his face, and the girl, 16, suffered a broken leg, police said. The car also caught fire.
Investigator Cory Carlyle said the incident began about 8 p.m. when the woman saw two young people who appeared distressed outside the grocery. She said she offered them a ride home, and after taking them to an address on Dunn's Lane, they said their mother would like to thank her.
After leaving the car to approach the house, she said one of the teens got behind the wheel, while the other strangled her from behind with a lanyard from her sunglasses.
She got away, but they got into her car and drove off. Police, however, quickly caught up with them and chased them through town with speeds approaching 75 to 80 mph.
The driver lost control of the car, crashing it into a porch at a residence at 297 Milledge Road.
Police said the two juveniles are facing multiple traffic and robbery charges when they are released from the hospital.