At the time he subjected his 34-year-old victim to the "prolonged and violent" sexual assault, Alexander Gallagher, 41, was on bail for breaking the terms of his release from a decade-long prison sentence for the rape of a woman as she sat in her car.
Gallagher faces the prospect of an order for lifelong restriction, a form of life sentence given for the most serious of offences.
His victim had to give evidence at his trial at the High Court in Glasgow after Gallagher pleaded not guilty, claiming the sexual contact had been consensual.
She told the trial that Gallagher forced her to have sex and then put a bag in her mouth to try to silence her screams.
Her ordeal in March last year also involved her being punched in the face, flung around the room and assaulted with a torch.
She was left battered and bruised as Gallagher walked out the flat.
Gallagher had only known his latest victim for a few weeks after being freed from jail on February 22 last year. He had been put on licence and ordered to wear an electronic tag.
By March 2013, the sex offender was back in the dock accused of breaking conditions of being on the Sex Offenders Register.
Despite his record, a sheriff bailed him and he was free to strike again just five days later.
The trial heard how Gallagher had been at the woman's flat in the south side of Glasgow with another man.
He claimed they had been listening to music before the woman went to bed. However, his claims that he joined her in the bedroom where they became intimate were challenged by the prosecution.
Sheena Fraser, prosecuting, questioned Gallagher about screaming that was heard during the attack, which he claimed had been consensual.
Miss Fraser went on: "Why did you put a carrier bag in her mouth to gag her?"
Gallagher, who denied putting the bag in his victim's mouth, claimed he hit the woman after they had sex, but only because she had assaulted him during a row over a phone.
Miss Fraser said it was clear he had "lost his temper".
Judge Lady Wolffe described the attack last March as prolonged and violent.
Jurors convicted Gallagher and he will be sentenced in November.
Prosecutor Sheena Fraser later challenged him about the victim being heard "screaming" during the attack. But Gallagher replied: "It was just noises from sex, nothing more. We were having consensual sex."
Jurors were unaware of Gallagher's past and were only told after the trial that he had been imprisoned for five years for assault and robbery in 1997.
He was freed in 2000, but 10 days later raped a mother-of-two as she sat in her car in Stirling.
He was jailed for 10 years, and also ordered to serve the remainder of his five-year sentence.
Prosecutors have also moved to have a risk assessment carried out on Gallagher, which could result in him being placed on an Order for Lifelong Restriction.