Using only the name Patricia, the woman alleged that Cosby drugged her twice. She spoke a day after President Obama said that giving anyone a drug in order to have sex without consent was rape.
CNN agreed to protect the woman's identity, and she appeared only in silhouette.
Also on CNN on Thursday, Barbara Bowman, one of the accusers who did the most to trigger the flood of allegations now dogging Cosby, said she was gratified by the President's statement.
But she said Obama should use an executive order to revoke the Presidential Medal of Freedom Cosby was awarded in 2002. Obama said Wednesday that there was no "mechanism" for revoking the medal.
Still, Bowman said that Obama, who has two daughters, was a strong supporter of rape survivors.
Cosby, through his lawyers, has denied all allegations of sexual misconduct.
Place settings for just two at 'dinner party'
Patricia said she met Cosby in the late 1970s, when she was a 22-year-old aspiring singer. She said the comedian invited her to his family home in Massachusetts for a "dinner party."
She said she expected to find family and friends in attendance. But when she arrived, she found only place settings for two on a coffee table, she said.
"The fact that we were alone did bother me," she said. "But I thought, he's a trusted man. I can trust him."
She said Cosby gave her a drink. Halfway through that one drink, she said, she started to lose her balance and slur her words.
And the next thing she was aware of, she said, was waking up naked in a bed, with Cosby standing over her, wearing a bathrobe.
He told her she had thrown up and passed out, she said. When she asked where her dress was, Cosby said he'd had to wash it, she said.
"To my knowledge, I'm the only person who's accounted for an episode that took place in his family home, in Shelburne Falls, Massachusetts, where he raised his family ..." Patricia said. "Whether it was with Camille's knowledge or not, I don't know," she added, in a reference to Cosby's wife.
She did not, however, say specifically during the interview whether she believed at the time that she had been raped.
Accuser: Cosby refused entry to his suite unless she took pills
In any event, she said, she saw Cosby again in Atlantic City, New Jersey, and, in her account, he invited her to his penthouse at a casino resort. But when she arrived, she said, Cosby refused to let her in unless she took the two pills he had in his hand.
"I said, 'What are they?' " she said. "He said, 'They're just something to relax you.' "
"I said OK because I wanted to spend time with this man who was offering to help me with my career," Patricia said.
Thirty minutes later, according to her account, she lost consciousness and did not come to until the next morning.
She was "naked, and I felt like somebody had penetrated me," she told CNN.
Patricia acknowledged that she did not go to authorities at the time.
"People didn't challenge powerful men in 1978, 1979 or 1980," she said. "They just didn't."
She also said that she believed Cosby had an obsession with Queen Noor of Jordan.
Before meeting her in Atlantic City, Cosby asked her to fix her hair the way Noor did, she said, adding that she had heard similar stories from others among Cosby's accusers.
Patricia said she was in some ways complicit in what happened. She wanted to advance her singing career, and she failed to listen to her intuition, she said.
But she added: "What he did was not right. And it was without my consent."