Sheffield Crown Court was told how just after 7pm on May 3 this year, South Yorkshire Police received reports of three men running from a black Astra vehicle that had crashed on Cemetery Road in Hatfield, Doncaster.
Two men were later arrested in connection with the incident.
Prosecutor, Neil Coxon, explained how in the early hours of the following morning, Albert Smedley phoned South Yorkshire Police to say the black Astra vehicle he had recently hired had been stolen while he was at the home of his friend, Louise Jani.
Smedley, aged 71, told officers that keys to the vehicle, which had been left on the side in the living room, were stolen during a sneak-in burglary while the pair were upstairs, as had the car itself.
Police came to Jani's home and the pair both made statements in which they repeated the same version of events.
On March 10, Jani, aged 31, and Smedley went to Doncaster police station and both admitted they had given officers false statements.
Mr Coxon said: "They said pressure had been put on Mr Smedley. He was aware of a traveller he only knew by his first name, who he had permitted to borrow the car.
"Louise Jani was aware of the individuals who had been arrested on suspicion of burglary, and didn't wish them to be sent to prison."
Both Smedley, of Stoops Lane, Bessacarr, Doncaster and Jani, of The Groves, Wheatley Hills pleaded guilty to a count of perverting the course of justice at an earlier hearing.
Defending Smedley, Andrew Smith, told the court: "The explanation he put forward was that someone he knew from his days as a user of drugs had effectively been bullying and pressuring him for three months."
Michael Cane-Soothill, defending Jani, said her life had unravelled after her grandfather was put on trial four years ago, which had led to her becoming involved with drugs and criminality. He said she had recently started a new life with a new partner, and wanted to put her offending behind her.
Judge Sarah Wright sentenced both Smedley and Jani to eight months in prison.
She said: "This offence undermines the course of justice, and must be marked by custody.
"The events are so serious that only immediate custody is appropriate."