"In my head, I was trying to get my hands to move or my legs to move, but I was frozen", she said.
She said Mr Cosby gave her pills he claimed were herbal to help her relieve stress over a possible career change.
"They're your friends," she recalled him saying when he handed her the pills. "They'll take the edge off."
Mr Cosby, 79, denies the charge while his lawyers claim she agreed to sex and has changed her story several times.
But Ms Constand said her vision started to blur about 20 minutes after taking the pills. Mr Cosby began groping her and placing her hand on his genitals, she said.
"I wasn't able to fight it in any way," she told the court. "I wanted it to stop."
She continued that she felt "humiliated" and "confused" after the alleged incident.
Before Tuesday's testimony, Ms Constand had been barred from sharing her story in public due to a confidential settlement she reached with Mr Cosby in 2006.
She received an undisclosed cash sum and her deposition from that lawsuit remains sealed.
Dozens of women say Mr Cosby assaulted them, but statutes of limitation rules mean he is on trial for only one allegation.
A mother of a witness who separately claimed Mr Cosby drugged and sexually assaulted her in a similar manner in 1996 also testified on Tuesday in Norristown, a suburb of Philadelphia, where the trial is being held.
"She changed considerably," Patricia Sewell said in court. "Her circle of friends became small. She had very little social life. Her self-esteem was very damaged."
Kelly Johnson, Ms Sewell's daughter, testified on Monday that he gave her a pill to "relax" during a meeting at his Los Angeles hotel room for career advice.
Ms Johnson, who worked for a talent agency representing Mr Cosby, alleges she woke up partially clothed in the comedian's bed with him behind her, grunting, before he forced her to touch his genitals.
Angela Agrusa, an attorney for Mr Cosby, grilled Ms Sewell on her account of the alleged incident, suggesting she may have heard the story during a television appearance in 2015 instead of 1996 after it allegedly occurred.
The case is seen as the biggest US celebrity court case since the murder trial of former American football player OJ Simpson in 1995.
Ms Constand says Mr Cosby drugged and molested her after she visited his home seeking career advice in 2004.
She was 31 at the time and had befriended him through Temple University in Philadelphia, where he served on the board of trustees.
Mr Cosby's defence lawyers argued on Monday that his encounter with her was one of many consensual, romantic episodes between them.
His legal team said he had only offered Ms Constand Quaaludes - a sedative widely used recreationally in the US in the 1970s - after she complained of having trouble sleeping.
She is expected to serve as a key witness for prosecutors during the two-week trial.
Mr Cosby's wife of 53 years was not seen with him as he entered the court in Norristown, near Philadelphia, on Monday or Tuesday.
But Keshia Knight Pulliam, who played his on-screen daughter in The Cosby Show, did accompany him on the first day.
Mr Cosby faces three counts of aggravated indecent assault. Each count carries a maximum sentence of 10 years and a fine of up to $25,000 (£19,500).
The comic - who was at one point the highest-paid actor in the US - has said he will not testify in the trial, which is expected to last about two weeks.
If convicted, Mr Cosby faces up to a decade in prison.
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