Jones, who in later years was a leader of the Norton Simon Museum, died at her home in Malibu of natural causes, museum spokeswoman Leslie Denk told The Associated Press.
Jones was the widow of the museum's founder, wealthy industrialist Norton Simon, and served as chair of the museum's board of directors after his death.
Known for her intense performances, Jones was one of Hollywood's biggest stars of the 1940s and '50s.
Among her most memorable roles were the half-breed vixen who vamps rowdy cowboy Gregory Peck in "Duel in the Sun," and the Eurasian doctor who falls for Korean War correspondent William Holden in "Love Is a Many-Splendored Thing."
Despite her heavily dramatic screen roles, Jones conveyed an aura of shyness, even aloofness offstage. She rarely gave interviews, explaining to a reporter in 1957: "Most interviewers probe and pry into your personal life, and I just don't like it. I respect everyone's right to privacy, and I feel mine should be respected, too."
Early in her career, Jones had become nearly as famous for her high-profile marriages as for her movie work. She met actor Robert Walker when both studied acting in New York, and they married and came to Hollywood, where her stardom ascended more rapidly than his.
Jones' boss, David O. Selznick, became obsessed with his star and spent much of his time promoting her career. They married four years after she divorced Walker in 1945.
Selznick died in 1965, and in 1973 Jones married Simon. After his death in 1993, she assumed a major role in leading the Pasadena-based museum.
She initiated the museum's celebrated gallery renovation by architect Frank Gehry and spearheaded the development of its public programming and outreach initiatives.
She was born Phylis Isley on March 2, 1919, in Tulsa, Okla., to parents who operated a touring stock company that presented melodramas in tent theaters in the Southwest. She began doing roles in their plays at the age of 6.
After graduating from a Catholic high school, she toured with another stock company, studied drama at Northwestern University for a year, then persuaded her father to support her for a year at the American Academy of Dramatic Arts in New York.
She married Walker in 1939 and they spent their honeymoon traveling to Hollywood. They could find only bit roles in small pictures, she in a western, "New Frontier," and a serial, "Dick Tracy's G-Men."
The pair retreated to New York before Jones was selected for the prize role in "The Song of Bernadette" about a French peasant girl who claimed to have seen a vision of the Virgin Mary at Lourdes in 1858.
Her performance and the Oscar for best actress helped make her one of Hollywood's most popular leading ladies.
Director Henry King recalled testing the six finalists for the role of Bernadette: "A man held a stick behind the camera; the girls focused their rapt attention on that stick. The other five did very well. But only Jennifer looked as if she saw the vision."
Among her other films were "Love Letters" (with Joseph Cotten), "We Were Strangers" (with John Garfield), "Madame Bovary" (with Louis Jourdan) and "A Farewell to Arms" (with Rock Hudson).
She received a supporting actress Oscar nomination for "Since You Went Away," and lead actress nominations for "Love Letters," "Duel in the Sun" and "Love Is a Many-Splendored Thing."
While in Rome filming "A Farewell to Arms," Hudson told a reporter, "I heard fantastic stories about this girl, that she was neurotic, temperamental, under hypnosis by Selznick. Not a word of truth in any of it. From the first take, she's been cooperative with everyone - except reporters."
Her last film under Selznick's guidance came in 1962 with F. Scott Fitzgerald's "Tender is the Night," a failure.
Several months after Selznick's death in 1965, she went to England to film "The Idol." As it turned out, she made only two more film appearances, in 1969's "Angel, Angel, Down We Go" and 1974's "The Towering Inferno."
Two years after she filmed "The Idol," a sheriff's deputy found Jones in the surf at Malibu. She was not breathing but still had a heartbeat and he was able to revive her.
She had earlier called her physician to say she was taking pills, and it appeared she had fallen from a cliff into the ocean.
Her daughter plunged to her death from the 22nd floor of a hotel in west Los Angeles in 1976, and tests showed traces of morphine, barbiturates and alcohol in her system. The death was ruled a suicide.
After retiring from acting after "The Towering Inferno," Jones avoided the limelight as much as possible.
She is survived by her son, Robert, eight grandchildren and four great-grandchildren.