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Harvey Weinstein Rape Accuser Jessica Mann Testifies ... Claims He Broke Her Down, Says She 'Owed Him'

Harvey Weinstein rape accuser Jessica Mann claims he began manipulating her as soon as he met her, forced himself on her multiple times and finally raped her ... and she said it all under oath.

The former actress took the stand and gave emotional testimony Friday, breaking down in tears as she described her history with the disgraced movie mogul ... including alleged sexual assaults.

Mann testified she met Weinstein at a party about 7 years ago, and he quickly took interest in her and began offering her work. Mann claims she had several meetings with him to discuss her career, but he asked her for a massage at an early meeting ... and forced oral sex on her at a later meeting in which she thought she'd be discussing a movie role.

Mann testified she faked an orgasm to get out of the situation.

Weeks later, Mann alleges Weinstein raped her at the hotel in Manhattan after injecting his penis with erection medication. She testified that he physically blocked her from leaving the room and made her undress. She says ... "I gave up at that point."

Mann says about a year later, Weinstein told her "She owed him one more time" after she informed him she had a boyfriend ... and claims he had intercourse with her.

Weinstein's side has argued the 2 had a consensual relationship that lasted years after the alleged sexual assault, and have pointed to several emails Mann sent to him in which she expressed affection and love.

Mann's the fifth accuser to testify in Weinstein's trial, in which he's accused of first and third-degree rape and predatory sexual assault.

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