Elizabeth Sherlock died of multiple injuries
Mark Woolley, 36, and Jackie Moorhouse, 24, then calmly walked from the scene arm in arm, according to the prosecution at the Old Bailey.
Their victim, 42-year-old Elizabeth Sherlock, died of multiple injuries outside London's Euston station on 16 April.
Mr Woolley, from Pentonville and Ms Moorhouse, from West Hampstead, deny murder.
Mrs Sherlock was drinking coffee with her husband, Peter, at a cafe at Euston station when her handbag was snatched.
Nicholas Horwell, prosecuting, said Ms Moorhouse went into the station looking for a potential victim, while Mr Woolley waited in the car outside "as the getaway driver, ready in case things went wrong".
He said Ms Moorhouse then stole the bag, but was followed moments later by Mrs Sherlock who showed "courage and determination" in running after her.
Escape blocked
Mr Horwell said Mrs Sherlock then placed the top half of her body across the couple's car to prevent them getting away.
Unable to dislodge Mrs Sherlock who was gripping the wiper blades, the couple drove into a side street but their escape route was blocked by a bus.
Mr Horwell said Mr Woolley was so determined to get away that he put the car in first gear and drove over Mrs Sherlock.
"Her body was dragged for a short distance and knocked about like a rag doll."
Tyres deflated
As they drove off a fireman threw his helmet at the windscreen.
The car also clipped a kerb, deflating both passenger side tyres.
"Some witnesses say the front and rear wheels went over her body.
"Some say just the front. But by the movement of the car, they must have known they had run over Mrs Sherlock," said Mr Horwell.
The couple were said to have abandoned the car, leaving the scene arm in arm.
'I have sinned'
Mr Horwell said police arrested them three days later.
Officers found a note in a jacket at their flat which read: "Dear Lord. I have sinned. Forgive me for a terrible sin. God rest the poor woman's soul."
A mobile phone belonging to Mrs Sherlock was found in another jacket.
Mr Woolley has also pleaded not guilty to stealing the handbag. His partner Ms Moorhouse also denies manslaughter.
The case continues.