Darren Ferris, 24, from Motherwell, lost control of his Ford Mondeo which hit 44-year-old Linda Carson in the town's Muirhouse Road on 27 September.
Mrs Carson later died at the scene from multiple injuries.
Ferris admitted causing her death by dangerous driving. He was jailed for nine years and six months.
Jailing Ferris at the High Court in Edinburgh, judge Lord Turnbull told him: "Your behaviour on that evening, when seen in the context of your previous offending, demonstrates you have no sense of the civilised values by which others in our community live their lives."
Lord Turnbull said Mrs Carson had been a mother and wife "in the prime of her life" who, through the random timing of taking her dog for a walk, found herself in the path of a drunk driver travelling at excessive speed.
He said the author of a background report on Ferris could "detect little by way insight or genuine remorse" on his part.
"The consequence of your conduct was predictable, but it was also truly tragic for Mrs Carson and her family," he said.
A previous hearing at the High Court in Glasgow was told that on the day of the crash Ferris had been drinking Buckfast and was "pretty drunk".
At about 20:00, Mrs Carson left her home in Gresham View, Motherwell, to walk the family dog.
Ferris was seen driving the Mondeo at excessive speed, causing some witnesses to remark that he was "flying past" and driving "like an idiot".
He then lost control on Muirhouse Road, causing the car to mount the pavement, hit Mrs Carson and then smash into a wall.
Afterwards, Ferris got out of the car and spoke to Mrs Carson who was lying on the pavement.
What he said was not heard, but a bystander then saw him put his hands to his head and shout before running from the scene.
One of the people who tried to help Mrs Carson called the mobile number on the dog's collar and spoke to 47-year-old Mr Carson.
He then rushed to the scene with their 11-year-old daughter and both were comforted by locals while a nurse attempted CPR on Mrs Carson until paramedics arrived.
The court was told that Mrs Carson died from multiple injuries.
Ferris was later seen dropping car keys from the window of his flat at Grange Tower, before police arrived and forced entry.
When he saw them he became aggressive, told them to leave and denied that he had been driving.
A breath test carried out on Ferris 90 minutes after the crash gave a reading of 63mcgs. The legal limit is 22mcgs.
Police experts who examined the crash scene concluded that blame for the fatal collision lay with Ferris who drove at an inappropriate speed in a 30mph limit area, under the influence of alcohol and failed to negotiate a right-hand bend.
Speaking after sentencing, Insp Darren Faulds, of Police Scotland, said: "Ferris, despite having already been banned from the road for a previous conviction, took the decision to get behind the wheel of that vehicle whilst under the influence of alcohol, and in doing so, had absolutely no regard for the safety of any pedestrians or other motorists in his path.
"Following the fatal crash, in an act of cowardice, he fled from the scene and tried to cover his tracks before being traced and arrested."
A man with two previous drink-driving convictions has been jailed for killing a woman in a crash while he was over the limit and flouting a driving ban.