Many of Mr Hulme's relatives were present at the hearing
A coroner said he hoped the "sad death" of a young father at the wheel of a stolen car would serve as a "warning to others".
Joel Hulme, 19, was over the drink limit and had taken cocaine before the crash in June, an inquest heard.
The disqualified driver from Swansea died at the scene after hitting a pedestrian island and rolling the vehicle onto its side.
Coroner Phillip Rogers recorded a verdict of accidental death.
The inquest heard that Mr Hulme passed a police panda car just after midnight on 21 June in a Vauxhall Cavalier that had been stolen from a car park at the city's Morriston Hospital two days earlier.
He appeared to speed up although police said the patrol vehicle did not give chase, the hearing at County Hall was told.
About two minutes later he was seen by a second police patrol car as he ran a red light and cut a junction on the wrong side of the road in the Llansamlet area.
Special constable Mark Ford told the hearing he then saw the Cavalier hit the pedestrian island.
"The car impacted that and lifted off the floor," he added.
It came to rest on its side trapping Mr Hulme against the road.
Officers tried to lift the vehicle off him but he already appeared to be dead.
Accident investigator Pc Nicole Cooper said Mr Hulme, from the Bonymaen area, was not wearing a seat belt which may have prevented him being partially eject from the car.
Coroner Mr Rogers said: "It was highly likely that some disaster would befall Mr Hulme that night - it's unfortunate that it was a fatal collision.
"I hope that the sad death of Mr Hulme will serve as a warning to others about the extreme dangers of the sort of behaviour we've heard about this afternoon."