Streisand had a star turn as Fanny Brice in "Funny Girl," a role she began on in a hit Broadway musical, while Hepburn, who won Best Actress the previous year for "Guess Who's Coming to Dinner," earned another win for "The Lion in the Winter."
Ingrid Bergman had the honor of presenting the award that year and after she opened the envelope she said, "It's a tie!"
The audience gasped and Bergman then revealed the two winners. Hepburn did not appear at the ceremony but Streisand was on hand to collect her award.
"Hello gorgeous," Streisand said, clutching the Oscar. She would go on to win a second Oscar in 1977 for Best Original Song for "Evergreen," the theme song to "A Star Is Born."
There had only been one previous instance of a tie back in 1932 when Fredric March of "Dr. Jekyll and Mr. Hyde" and Wallace Beery of "The Champ" tied for Best Actor.
Leading up to the ceremony, "On The Red Carpet" co-host Rachel Smith will be doing interviews with hair and fashion stylists and makeup artists for the "Best Dressed" video series featured on Oscar.com, beginning on Feb. 11. Smith will also be covering live events and offering post-show analysis of Oscar night fashions for the site.
It was announced in November, that Billy Crystal would return to host the 84th annual Academy Awards.
The awards ceremony will air live on Sunday, Feb. 26, 2012 on ABC7. Coverage begins at noon PT.
OnTheRedCarpet.com will have complete coverage of the Oscar season, including an exclusive interactive live stream show LIVE from the red carpet. Follow @OnTheRedCarpet on Twitter and "Like" On The Red Carpet on Facebook, and download our FREE entertainment news app for the iPhone and iPad.