Matthew Cawston, 27, attacked the woman while she was asleep, with her child also asleep next door, and the victim now suffers nightmares and flashbacks.
The man has been sentenced to 10 and a half years in prison.
Cawston knew the victim and had been called to help with a domestic emergency at her home.
But when the job finished, he said he didn’t want to cycle home in the rain and asked to stay the night, Preston Crown Court heard.
The woman agreed to let him stay on the sofa, but made it very clear she didn’t want to have sex with him, said prosecutor, Paul Treble.
The woman went to bed and left Cawston on the sofa, but later woke to find her pajama bottoms had been removed and Cawston lying on top of her having sex.
In a statement, she told police she “froze”, adding: “He was trying to be as gentle as possible and as quiet as possible so as not to wake me.”
Her young daughter had been asleep in the room next door.
In a victim impact statement, the woman said she has suffered from nightmares and flashbacks and had felt she had to move house following the attack.
She no longer invites visitors into her home and does not feel safe going out.
She said: “Because he was sexually frustrated he has completely destroyed my confidence and trust in people and seriously affected my mental health.
“I can never put into words the true effect this has had on me, my daughter and my family, and will continue to have for a very long time – possibly forever.”
A few days later after the attack, the victim texted him, asking: “Why did you do it? You had sex with me while I was asleep?”
The defendant replied: “I was horny. Sorry.” and asked if she was going to report him. The woman later told a college tutor and then the police.
Cawston, of Blackpool, was arrested and insisted he had never had sex with the woman without her consent.
However, he later pleaded guilty to rape.
Barbara Webster, defending, said Cawston has Autistic Spectrum Disorder and receives support from a social worker.
Ms Webster said: “It does not excuse what he did but it gives an insight into his behaviour.”
Sarah Armstrong, a social worker, said Cawston had “difficulties understanding relationship boundaries” and was “significantly exploited by people, both financially and materialistically, who he considered friends”.
Judge Sara Dodd, sentencing, said: “It is very clear to me that this offence has had a great impact on your victim.
“She described feeling like her life is on hold and can’t move forward until justice is done. I have also to consider the fact you are still a very young man and you have no previous convictions.
“Your own mental difficulties, your autism, no doubt played a significant part in your offending. I accept your remorse in this case is genuine.”
However, she said Cawston posed a very real risk to adult women he was in a relationship or friendship with.
Judge Dodd sentenced Cawston to ten years and five months, comprising of six years and five months in custody and a four year extended licence.
He cried as he was led away to the cells.