Maureen Ashley, 65, started following the youth, who was on a bicycle, but lost control and grazed a lamppost before the car came to rest against a fence.
The retired probation officer was charged with dangerous driving, which carries a maximum five-year sentence.
But after waiting eight months for the case to be heard, a court accepted her guilty plea to the lesser charge of careless driving.
She was fined £500 with £200 costs and given eight penalty points on her licence. Mrs Ashley, a widow from Leagrave, near Luton, declined to comment after the hearing.
But her son Graham, 40, said the case 'should never even have got to court'.
He added: 'She just wanted it to be over. She's never been in trouble before.'
The mother of three had just parked near her home on July 21 last year when the youth yanked open the passenger door of her car and grabbed her handbag.
She dialled 999 before giving chase. She did not exceed the speed limit but lost control when she leaned over to shut the passenger door. The youth has never been caught.
Roger Carne, defending at Luton Crown Court, said Mrs Ashley - who had driven for 37 years without incident - 'is a pillar of society and has suffered great distress from this matter'.
Judge Richard Foster told Mrs Ashley on Tuesday it was a 'tragedy' to see her in the dock.
'You saw someone steal your handbag and rather than simply give in to that behaviour you started to pursue that person, which in its own way is admirable,' he added.
'But you did it in a car and the safety of other road users and pedestrians is more important than your handbag.'
There we go the righteous have enforced the law, justice as they see it has been handed out. A criminal has been processed and Gordon the great can claim that crime is falling. Never mind that the justice system routinely turns the ordinary citizen into the criminal for the most petty of so called offenses, that concepts of fairness and decency have been replaced by hard stalinist lines of rules and fixed penalties.
One day the madness of King Gordon will come to an end, that day can not come soon enough for my liking.