Presenting a tribute to Redford during In Memoriam section of the awards ceremony, Streisand described the late star as a “brilliant, subtle actor”.
Streisand, who starred with Redford in 1973 drama The Way We Were, said:
“We had a wonderful time playing off each other, because we never quite knew what the other one was going to do with the scene.
Barbra Streisand paid tribute to Robert Redford at the Oscars (Chris Pizzello/AP)
“And I’m thrilled that The Way We Were is now considered a classic love story, but it’s also about a dark time in our history, the late ’40s and early ’50s, when people were informing on each other and subject to loyalty oaths.
“Now, Bob had real backbone on and off the screen.
“He spoke up to defend freedom of the press, protect the environment and encourage new voices at his Sundance Institute, and some of whom, some of whom are up for Oscars tonight, which is so great.”
At the end of her tribute she launched into a rendition of the theme song from The Way We Were.
Redford, who was known for films such as Butch Cassidy And The Sundance Kid and The Sting, also won a best director Oscar for Ordinary People in 1980.
He died in September at the age of 89, with Streisand describing him as an “intellectual cowboy who blazed his own trail and won the Academy Award for best director”.
“And I miss him now more than ever, even though he loved teasing me,” she added.
Other stars to be remembered during the sequence included Diane Keaton, Rob Reiner, Catherine O’Hara, Pauline Collins, Giorgio Armani, Tom Stoppard and Terence Stamp.