Andrea Carr, 47, was given a ten-month sentence after a court heard how the pensioners suffered life-changing injuries in the collision.
Leeds Crown Court was told Carr worked for a home care company on a zero hours contract.
Her lawyer described how Carr and her colleagues worked under pressure and were given work schedules and appointments that are "simply not realistic."
Richard Walters, prosecuting, said the collision happened on the morning of September 16 last year on Carlton Road, South Elmsall, near Pontefract.
The prosecutor said Carr had been late for an appointment at the home of an elderly client earlier that morning and was also running late for a meeting with colleagues.
Mr Walters said Carr cut a corner to beat traffic lights on Barnsley Road before turning into Carlton Road and knocking the women down as they crossed.
He said: "The lights were changing and she tried to beat them.
"The Crown suggest that, together with the fact that she was late, contributed to this because she had a good field of vision.
"For whatever reason she did not see these two old ladies in the road."
The women, aged 78 and 82, were friends and were on their way to go shopping.
One suffered a fractured skull, spinal injuries, a dislocated shoulder and a bleed to her brain.
The other woman suffered spinal injuries and a dislocated ankle.
The prosecutor said: "Both ladies suffered terrible injuries. From being reasonably fit, they are now totally dependant on others."
Carr stopped immediately after the incident and dialled 999.
Mr Walters said: "She was crying hysterically and begged the operator to help."
She said to the operator: "I hope to God they are alright."
Carr, of Clifford Road, South Kirkby, pleaded guilty to two offences of causing serious injury by dangerous driving.
Marcus Waite, prosecuting, said the mother-of-two had no previous convictions had worked hard to support her family.
He said Carr accepted she was at fault and had pleaded guilty at the earliest opportunity.
Mr Waite said: "The defendant is someone who cares for vulnerable people.
He added: "She would change places with the victims in a heart beat if she could."
Describing Carr's working conditions he said: "The defendant says that she her colleagues who do the same role work under pressure and are set timescales and appointments and they are simply not realistic."
Jailing Carr, judge James Spencer, QC, said: "I have to explain to you and also to the public what I am doing because this is an important case.
"I know South Elmsall. It is a small village and everybody knows everybody else and so everybody will know about this incident. It is right that they know what is going through my mind.
"For those few minutes you drove your car dangerously because you drove your motorcar in a way that was far below the way a prudent driver would be expected to do so.
"You did not look where you were going.
"You mowed those two women down. It is a tragic incident. They were very seriously injured and what independence they had has been knocked out of them. They have been hospitalised and their lives have changed considerably."
The judge continued: "I also take in to account that you were immediately remorseful and I know what impact that 999 call had on those who had listened to it.
"You immediately recognised what you had done. You are a hard working woman and have worked hard all your life. You have no previous convictions and people speak highly of you.
"But it does seem to me that this offence, this piece of driving, merits a prison sentence.
"I regret having to send you to prison but I feel I must."
After the case, John Cafferty, Yorkshire and Humberside Regional Secretary for public service union UNISON, said: “This was a tragic accident and our sympathies go out to everyone who has been so badly damaged by it.
“One of the most caring people in society has been sent to prison and two elderly women have been seriously injured.
“This carer was on a zero hours contract - under impossible time pressure to see all the people who depended on her skill and dedication to survive- when the accident happened.
“UNISON has always fought against the privatisation of public services, including community care for the most vulnerable, because private companies must make profits for shareholders. They cut wages and service standards because they have to make profits for their shareholders.
“That puts care workers under intolerable pressure. Low wages, insecure jobs, the stress that all carers cope with every working day, all take their toll on their health and well-being.
“This tragic event must surely take the desperate need for increased central government funding for public services to the top of the political agenda. Privatisation and zero hours jobs have terrible consequences.”