The victim was taken to the south Asian country on the pretence that she and her family would celebrate Eid together, but was instead told by her parents that they had set up a wedding for her.
The teenager, who was 18 at the time of the incident in July 2016, was left "almost suicidal" by the proposition and was supposedly told by her mother that she would have to have a child with her would-be husband so that he could attain a visa.
During her evidence, the victim, from Leeds, claimed her father threatened to "chop her up in 18 seconds" if she did not agree to the plan.
She also told how he would repeatedly beat her, at her mother's encouragement, after saying she did not want to marry the relative.
"I thought, if the worst came to the worst, then I would get married and come back to England, and file a report saying what had happened," the victim said.
"But my mum said there was no way that that would happen, because they were going to leave me there for a year so that I would get pregnant so that he (the first cousin) could get a visa."
With the help of her sister and boyfriend, she was able to contact the British High Commission who, fearing she may be in danger, performed a rescue operation days before the marriage was due to take place.
Following a trial at Leeds Crown Court, her parents were convicted of forced marriage and of using threats, violence or coercion to pressure her into going through with the wedding.
They are due to be sentenced at the same court on Monday morning.