Liam McDonagh was jailed for 16 months at Leeds Crown Court over the incident on North Street on November 9 this year
McDonagh was seen by police officers driving a Vauxhall Insignia which they suspected had been fitted with cloned plates.
The officers followed the vehicle along Kirkstall Road but the defendant refused to stop despite officers putting on blue lights and sirens.
McDonagh drove at 90mph in a 30mph area and went through red lights at the junction of Cardigan Road.
He drove through another red light at a pedestrian crossing at 80mph before joining the A58 inner ring road.
The 24-year-old continued to drive dangerously, reaching double the speed limit and causing other cars to brake to avoid a collision.
McDonagh then took the exit slip road towards North Street and collided with a sign post before driving into the back of a Transit van at traffic lights.
He ran from the car after the collision but was chased and caught by the police officers.
The driver injured his hip, back and pelvis in the collision.
McDonagh was interviewed and gave a statement in which he claimed he had been a passenger in the car and not the driver.
He pleaded guilty to dangerous driving, driving while disqualified and having no insurance.
The court heard he has previous convictions for vehicle theft and careless driving.
Andrew Petterson, mitigating, said McDonagh had been in custody since his arrest.
Mr Petterson said his client pleaded guilty at an early stage and accepted he would receive a prison sentence.
McDonagh was also banned from driving for 36 months.
Judge Simon Phillips QC said: "This was an appalling piece of driving and that is no overstatement.
"I wonder if you ever paused for a moment, Mr McDonagh, to consider if some pedestrian might have been on that crossing.
"If they had been struck at that speed they would have been killed.
"It was a matter of fortune not judgement that someone was not killed or injured."