Stephen Richards appeared drunk as he was helped from the wreckage of his Audi A3 after it flipped onto its roof during the crash on Leeds Road, Scholes.
Richards, 38, has a long history of driving offences despite never having held a driving licence.
Leeds Crown Court heard Richards lost control of his step-father's car at a bend in the road and struck a kerb before veering into the opposite carriageway.
His car then hit a Honda Civic in which the couple were travelling before landing in a ditch.
Bashir Ahmed, prosecuting, said other motorists stopped to help Richards from the vehicle but he ran off.
The prosecutor said witnesses described how Richards was slurring his words and appeared incoherent.
He was identified after his blood was found in the car and CCTV footage captured him running away.
Richards was arrested and interviewed but told officers: "It's nowt to do with me."
The couple both needed hospital treatment after the collision, which happened on November 4, 2016.
The husband, who was driving, suffered injuries to his knees and back.
He also lost teeth as a result of the impact of the crash and was unable to work for two months.
His wife suffered injuries to her legs and back and was in severe pain.
She described in a statement how she had suffered from anxiety and had been unable to sleep properly in the months after the incident.
Richards, of Pembroke Towers, Gipton, Leeds, pleaded guilty to causing serious injury by dangerous driving, having no licence and having no insurance.
The court heard Richards has previous convictions for driving offences dating back to 2001.
In 2002 he was convicted of dangerous driving after he was involved in a high speed police chase through busy streets as schoolchildren were in the area.
He also has convictions for drink driving.
Michael Walsh, mitigating, said: "The incident almost speaks for itself. The only mitigation for Mr Richards is his guilty plea."
Mr Walsh said the father-of-two was a carer for his parents and his relatives would suffer if was sent to prison.
Jailing Richards, Recorder Carl Gumsley said: "You have absolutely no respect for driving. You have no respect for the rules of the road. You have no respect for the rule of law.
"I accept that people will be effected by this but this is your fault, not anybody else's fault."
Richards was also banned from driving for four years.