"The books were porn, which I'd never seen before. Hardcore porn," the 81-year-old said in the documentary.
"The next thing I knew, I was out flat on the sofa in that living room and he was raping me. And what he had given me was a drug. He had drugged my drink.
"It was what is called in those days a Mickey Finn. Which I think today would be Rohypnol. It felt so horrible. That I... That I'd done this thing."
Her story comes amid allegations made by numerous women that Bill Cosby drugged and sexually assaulted them - claims his lawyers have firmly denied.
Out of shame and guilt, Collins continued her relationship with Reed and eventually agreed to marry him. She remembers crying on the evening prior to her wedding, but her father told her that people had already been invited so it was best to go through with it.
"It wasn't my fault but I didn't know, I went out with him. And maybe I shouldn't have gone out with him. He was much older than me, and he was a famous star," she said.
"And anyway the bottom line is that he called me, and I went out with him again. And after I'd been going out with him for a few months, he asked me to marry him.
"And I thought, 'Well I better because you know, he took my virginity.' I really hated him, but I was so filled with guilt, that he had done this thing to me."
The couple divorced four years later in 1956. The incident, unsurprisingly, haunted her for a while to come.
"It took a long time to be able to really trust any man," she said.
Collins has been married five times, and is currently wed to husband Percy Gibson since 2002. They renewed their vows in 2009.
- Independent