The film is based on the book of the same title by Pearl's widow, Mariane Pearl (with Sarah Crichton), and told from her perspective.
Jolie, who portrays Mariane, told the audience at the Museum of Tolerance that throughout the filming she was constantly aware of the Pearl family's "unimaginable suffering."
"I hope we have done right by you," she told the reporter's parents, Dr. Judea and Ruth Pearl.
The Paramount Vantage film, which opens June 22, was directed by Michael Winterbottom and co-produced by Brad Pitt. Jolie and Pitt are also partners in private life and the parents of four children.
The preview raised $15,000 for the Daniel Pearl Foundation, established by the Pearl parents to promote understanding between different cultures and religions. The event was also sponsored by Artists for Amnesty.
Speaking of his 5-year old grandson Adam, born a few months after his father's slaying, Judea Pearl urged the boy to keep his faith in humanity, despite all obstacles.
Ruth Pearl said she hoped that her son will be remembered for the way he lived and worked, rather than the way he died.
Daniel Pearl was decapitated in Karachi in January 2002, but although four Islamic terrorists were quickly convicted of the crime and are appealing their sentences, new alleged accomplices continue to turn up.
Only last week, Pakistani police arrested two additional suspects, who, police say, are linked to Pearl's kidnapping and death.
In March, the Pentagon released a transcript of the interrogation of Khalid Sheikh Mohammed, the alleged al-Qaeda mastermind behind the Sept. 11 attack, and now held by the U.S. military at Guantanamo Bay.
According to the interrogation transcript, Mohammed said that he had personally beheaded Pearl, boasting that "I decapitated with my blessed right hand the head of the American Jew, Daniel Pearl."
-- Tom Tugend, Contributing Editor