A Labour AM has told an assembly debate about her experience of being assaulted when she was 18-years-old.
Jenny Rathbone said she was beaten around the head by a man who she drove home from a party, after she refused to go into his house.
"If we don't speak up then people who are seriously disturbed will go on doing this sort of thing," she said.
The Plaid Cymru debate called for the devolution of criminal justice to deal with low rates of rape convictions.
During the debate Ms Rathbone, the AM for Cardiff Central, described an incident that took place when she was a teenager.
"I gave a lift to a young man from a party," she said. "I'd never met him before and knew nothing about him, he just happened to live close to where I did.
"And when I dropped him off at his house and I refused to go in he started beating me around the head, from nowhere.
"I was perfectly okay, I ran off and left my car and then went back for it later."
She said she never reported the incident to anyone, including her parents or friends.
"How deeply disturbed was this individual, who I'd never met before and never have met since, that he thought he had a right to beat me over the head simply because I refused to go along with his advances?
"So, all of us must have had a similar experience, and how many other people did that man do that sort of thing to, and how many of them succumbed to it?"
'Survivors not believed'
Leanne Wood, Plaid AM for Rhondda, said: "Too often, survivors are not believed and are forced to relive horrific experiences through insensitive court processes and a culture that just doesn't believe victims."
Devolved powers could be used "to ensure that sexual assault support and services" are "available and well-funded," she said, "and for courts to be adapted so that victims feel protected, not intimidated when giving evidence".
A Plaid motion, calling for the devolution of justice to address low conviction rates, passed the assembly with 35 votes to 12, with two abstentions.
The UK government has previously said it would be too costly to devolve justice to Wales.
"It is our belief that a single jurisdiction is the most effective way to deliver justice across England and Wales," said a spokesman last year.