John Henderson struck Audrey Gray with the vehicle and ran over her in the fatal incident in McGregor Street, Drumoyne, Glasgow, shortly after he had been at a Rangers match on May 4 last year.
A senior judge told Henderson at the High Court in Edinburgh: "I don't think I can do other than impose a custodial sentence in your case."
The Lord Justice Clerk, Lord Carloway, said: "I take into account the fact that you are a first offender and I accept also you are a hard-working person who before this event led a blameless life."
The judge said: "I also take into account the conduct of the deceased, which was undoubtedly reprehensible in the manner she approached your car."
But Lord Carloway said he had to sentence on the verdict of the jury.
He also banned Henderson, 55, of Holmpark, Bishopton, from driving for five years.
Henderson was earlier found guilty of causing the death of Miss Gray, 50, of Aboyne Street, Glasgow, by driving dangerously, by causing his vehicle to collide with her and driving over her.
His trial heard the incident happened after Henderson had left Ibrox stadium, where Rangers had celebrated winning the Division Three title.
Miss Gray had been spotted shouting towards his car before the fatal incident.
Miss Gray appeared to continue yelling at Henderson and his friends as they got in the car.
Jobeth Boyle told the court how she witnessed her friend being hit by the car and said: "When he turned the wheel the side of the car hit her, then drove over her and then away."
She called an ambulance and other passers-by went to the aid of the victim but she never recovered.
During the trial Henderson had claimed that the car lurched forward after his foot slipped off the clutch while he was adjusting his seat.
Prosecutor Bruce Erroch said his claims of what happened that day were not those of a careful and competent driver. Henderson replied: "I am a careful and competent driver."