Dylan Jenkin, 18, was being pursued by a police car in Edinburgh when he hit 33-year-old mother-of-one Jill Pirrie on 12 May.
Jenkin, who held only a provisional licence and had bought the car online for £40, last month pleaded guilty to causing death by dangerous driving.
At the High Court in Glasgow, judge Lord McEwan sentenced him to six years in a young offenders’ institution for the actions that led to the “unmitigated tragedy”.
Jenkin sobbed as the judge described how Ms Pirrie, mother to five-year-old Matthew, had finished a shift at Edinburgh Royal Infirmary and was making her way home on Kingston Avenue when she was struck from behind and thrown against a wall.
Jenkin’s driving and the condition of the car, which had been registered off-road, had earlier caught the attention of police officers, who pursued him in a marked vehicle and signalled to him to stop.
Instead of stopping, he drove off at “high and excessive speed” and police lost sight of the car.
Lord McEwan said that after hitting Ms Pirrie, “you did not go to help her but ran away across a nearby golf course”.
Ms Pirrie was taken to the hospital where she worked but died of multiple injuries. Jenkin was traced the next day as he sought medical treatment himself.
His three passengers in the car, bought from the Gumtree website, were also hurt.
The judge said impact statements from the nurse’s parents and her partner had made “heartbreaking” reading.
He said he took into account Jenkin’s upbringing, which had been “blighted by gross parental shortcomings,” but had found few mitigating factors for the crime.
The teenager, who has no previous convictions but was on bail at the time of the crash, was disqualified from holding a driving licence for seven years.
The court heard Jenkin had been “distraught and remorseful” since the crime.
Defence counsel Brian McConnachie QC said: “He has indicated that he will never be able to forgive himself for his actions.”