Fraser scooped the best cinematography award for Dune, joining best actress DeBose on the winners' list.
Fraser, whose other credits include Lion and Zero Dark Thirty, becomes the the seventh Australian to win an Oscar for best cinematography.
DeBose played the spirited Anita, who sings America in Steven Spielberg's remake of the classic musical.
As she held her gold statuette, the Afro-Latina actress asked the audience to imagine her as a young girl "in the back seat of a white Ford Focus".
"You see a queer, openly queer Latina, who found her strength in life through art. And that's what we're here to celebrate," she said.
"So, anybody who's ever questioned your identity. Or find yourself living in the grey spaces, I promise you this: There is indeed a place for us," she said, referencing the moving song from West Side Story.
DeBose also thanked "divine inspiration" Rita Moreno, who earned the best supporting actress award in 1962 for playing Anita in the original movie version of the musical.
Beyonce opened the show by performing Be Alive, an Oscar-nominated song from the movie King Richard, about the father of tennis stars Venus and Serena Williams.
She and her backup dancers, clad in sparkling yellow gowns, performed from a tennis court in the sisters' hometown of Compton, California.
After going three years without a host, a trio was chosen to guide Sunday's ceremony: Amy Schumer, Regina Hall and Wanda Sykes.
"This year, the Oscars hired three women to host because it's cheaper than hiring one man," Schumer joked.
A dark western, New Zealand director Jane Campion's The Power of the Dog, is battling feel-good deaf family drama CODA for the prestigious best picture prize.
Jessica Chastain, Nicole Kidman and other nominees donned a rainbow of colours for a ceremony with 2500 gown- and tuxedo-clad attendees and free from last year's pandemic restrictions.
Australian nominee Kodi Smit-McPhee - up for best supporting actor for The Power of the Dog - wore a light blue suit, while Chastain picked a lavender and gold gown with giant ruffles on the skirt.
Kirsten Dunst and Marlee Matlin chose bright red.
King Richard star Smith is the best-actor favourite for his role as the determined father of tennis legends Venus and Serena Williams. Competitors include Benedict Cumberbatch (The Power of the Dog) and Andrew Garfield for musical Tick, Tick ... Boom!.
Best actress is the most unpredictable. Many experts say Jessica Chastain's portrayal of TV evangelist Tammy Faye Bakker will triumph, though some give the edge to former Twilight vampire Kristen Stewart, who played Princess Diana in Spencer.
Nicole Kidman is also in the running, for her portrayal of US comedy legend Lucille Ball in Being the Ricardos.
Eight Oscars were presented in a pre-recorded segment of the show.
Dune collected four gongs - for sound, editing, production design and score for composer Hans Zimmer - with Melbourne-born Fraser taking that tally to five by picking up the award for best cinematography.
