The father was jailed for four-and-a-half years and the mother for three-and-a-half years at Leeds Crown Court.
None of individuals involved in the case can be named.
The woman was taken to Bangladesh with other family members for what they had been told was a holiday.
But the parents had made extensive plans for her wedding to a first cousin.
She reacted against the plan and her father hit her, with her mother’s reinforcement, the court heard.
Her father said he would “chop her up in 18 seconds” if she continued to reject the proposed marriage, the judge was told.
The woman managed to alert the police through her boyfriend in the UK and the court was played just a few of the messages she left on his phone.
Judge Simon Phillips QC said of the recordings: “Her terror and distress is palpable.”
Judge Phillips heard how the woman escaped with only the clothes she was wearing and a Leeds bus pass.
The woman said: “I was betrayed by the two people who are supposed to protect, love and keep you safe.”
She was born in the UK, lived a Westernised-lifestyle and was eager to go to university, the court heard.
Dafydd Enoch QC, defending her father, told the court: “These events are not borne out of malice, hate, greed or prejudice. They were borne of deep-seated culture.”
The pair were found guilty of forced marriage and a count of using violence, threats or pressure to force their daughter into marriage, following a three-week trial earlier this year.
Peter Mann, from the Crown Prosecution Service, said “This successful prosecution and the custodial sentences imposed send a clear message that forced marriage is a very serious crime and those responsible will be prosecuted.”
It is thought to be only the second case of its kind.
