Serial offender Dennis Reynolds stole the vintage red Saab after the owner accidentally dropped the key, before later crashing it into several other vehicles on Holbeck Hill, Scarborough, in the early hours of April 18 last year.
Jamie Palliser had also been in the passenger's seat when the crash occurred, which wrote off two other cars, before both offenders ran from the scene leaving the key in the ignition.
York Crown Court heard how both men had been caught after forensics officers combed the scene and found DNA on the car's deployed airbags, which hit a match on the UK DNA database.
Both were sentenced today (Friday) for their parts in the crime, which resulted in the Saab owner losing his "pride and joy" due to his insurance company not paying to cover the damage, meaning the car had to be scrapped.
Matthew Collins, prosecuting the case, said neighbours had awoken at 1.30am to a loud bang.
"When officers arrived, a red Saab had collided into a parked white Volkswagen car," he said.
"The engine was still running and the keys were in the engine. Both front doors were left open and the airbags had deployed. There were no occupants inside at the time, despite a neighbour having seen two males stagger away from the scene shortly after the bang."
Mr Collins added that a number of other vehicles had been damaged in the crash, including a white Kia which was written off completely, and damage of £300 caused to the brick wall it crashed into.
"The officers at the scene initially had very little to go on, except that the airbags were examined for DNA and compared against the national database.
"Palliser's DNA was found on the passenger's airbag, and Reynolds' DNA was found on the driver's airbag."
Kevin Blount, for Reynolds, said his client was currently undergoing grief counselling after losing his father some years previously, with the anniversary of the death in April around the time of the offence when he "struggled most".
Recorder Andrew Dallas, sentencing both, said the car had been "a classic car" which had been "much-loved" by its owner, adding that the crash had led to two other vehicles being damaged beyond repair causing "great stress and inconvenience".
Reynolds, 39, of Pavilion Terrace, Scarborough, was ordered to serve ten months in total for the crime after pleading guilty to aggravated vehicle taking, driving offences - namely, driving without insurance, without a licence and failing to stop at the scene of an accident - and subsequent drugs offences. He was also banned from driving for 15 months.
Palliser, 26, of Westway, Eastfield, received one month after pleading guilty to being carried in a stolen vehicle.