Christopher McKeown forced himself on his victim shortly after she had returned from celebrating her 21st birthday.
The £55,000-a-year engineer pounced as he prowled bedrooms of the house in Barrhead, East Renfrewshire for women to have sex with.
A jury heard how the attack left the victim badly affected as she was forced to quit university and her job.
McKeown is now behind bars after he was found guilty of rape following a trial at the High Court in Glasgow.
The 30-year-old will be sentenced when he returns to the dock next month.
The court heard how the young woman and a number of others - including friends, McKeown and an off-duty police officer - had gone back to her home after a birthday night out in October 2012.
The victim had not met McKeown before that evening.
Soon after arriving, he tried to kiss one of the woman's friends. Another friend called him a "creep".
The jury heard the student was later in bed when she was awoken by McKeown having sex with her.
He demanded she shut up as he held her on the bed.
Recalling her ordeal, she said: "I was trying to scream, but I just could not bring myself to.
"I don't know what would be normal for someone who has fought off a rapist - everyone reacts in a different way.
"I begged him to stop ... I was pleading telling him to stop, stop."
The victim eventually bit hard on his lip to get him away. She told the court: "It was the only thing I could do. I didn't have any other control over the rest of my body. I could not get away from him."
McKeown, also of Barrhead, then left the woman and was seen kissing one of her friends as she slept before being ordered out.
The victim - who suffered bruising to her torso and shoulder from the ordeal - was described as "manic" afterwards. She told the court how she struggled personally following the attack.
She said: "Life changed a lot - I dropped out of university, my job and I lost a lot of friends."
McKeown was later arrested by police and claimed anything that happened was consensual.
He insisted he had chatted with the woman before "one thing led to another".
Asked why he had gone in the victim's room, he claimed: "I knew there was somebody in there and I just went to chat her up a bit."
However, in her closing speech to the jury, prosecutor Jane Farquharson said the rapist "took advantage of the woman for his sexual lusts".
She added: "His actions and reactions are predatory. He knows what he wants and it would appear he was not to be stopped moving from one girl to another. Trying his luck and preying, I would suggest, on sleeping women."
Judge Edward Bowen QC deferred sentencing until next month at the High Court in Edinburgh.