Richard Hunter-Smith and Lee Andrew Morton broke into her Knottingley home, before stealing her car.
It took place in the early hours of 1 September last year, Leeds Crown Court was told.
Hunter-Smith, brandishing a knife, threatened to cut the lady if she did not meet his demands for cash and her car.
The pair then fled the scene in the victim’s car which was later found crashed on the driveway of a nearby property.
Hunter-Smith, aged 26, of Sycamore Avenue, Knottingley was jailed for 21 years after being found guilty of aggravated burglary and theft of a motor vehicle at an earlier trial.
He received an 11-year sentence for those offences, and a further 10-year sentence for grievous bodily harm with intent following a separate incident which happened at a take-away food shop on High Street, Knottingley on 13 September last year.
On that occasion Hunter-Smith was part of an attack in which the male victim’s thumb was cut off with bolt cutters and he was slashed with a machete.
Hunter-Smith was told he would have to serve at least 14 years in prison before he would be eligible for parole.
Morton, aged 41, of no fixed address, was jailed for four years and nine months for the burglary and theft of a motor vehicle.
Speaking about the burglary after the sentencing, Detective Constable Rebecca Greenwood of West Yorkshire Police’s Wakefield Adult Safeguarding team, said: "What these individuals did to a vulnerable victim that morning was truly dreadful.
"A crime like this would undoubtedly have an enormous impact upon anyone, but to subject a 75-year-old female who lives alone to this in her own home, depriving her of her car, her lifeline and her independence is just incomprehensible.
"I am pleased that these sentences reflect the severity of the crimes and hope that knowing these perpetrators will spend a significant time behind bars will bring some piece of mind to the victim."