Martin Scorsese's The Aviator came away with the most Oscars, its five awards including the supporting actress prize for Cate Blanchett.
Eastwood, who at 74 became the oldest directing winner, noted on Sunday night that his mother was with him when his Western Unforgiven won the 1992 best picture and directing Oscar.
"She's here with me again tonight, so at 96, I'm thanking her for her genes," Eastwood said. "I figure I'm just a kid. I've got a lot of stuff to do yet."
The 77th Oscars were another heartbreak for Scorsese, who lost the directing race for the fifth time.
Swank became a double Academy Award winner after her previous win for Boys Don't Cry, while Jamie Foxx took the lead actor prize for Ray.
The wins for Freeman and Foxx made it the second time African Americans won two of the four acting prizes.
Swank again beat out main rival Annette Bening, nominated for the theatre farce Being Julia.
"I don't know what I did in this life to deserve all this. I'm just a girl from a trailer park who had a dream," said Swank, who played an indomitable boxer.
Foxx won for his uncanny emulation of legendary musician Ray Charles in Ray. As he had at earlier awards triumphs, Foxx led the Oscar audience in a rendition of the call-and-response chant from Charles' 1959 hit What'd I Say, whose funky electric-piano grooves play over the opening credits of Ray.
"Give it up for Ray Charles and his beautiful legacy. And thank you Ray Charles for living," said Foxx, who climbed to Oscar glory after an early career built mainly on comedy.
Jamie Foxx lifted the trophy for
Best Actor for his role in Ray
Foxx had been a double Oscar nominee, also picked in the supporting category for the hit-man thriller Collateral.
Playing Katharine Hepburn in The Aviator, Blanchett had the spirit of the Oscars' most honoured actress on her side. Hepburn earned 12 nominations and won a record four Oscars in her lifetime.
"Thank you, of course, to Miss Hepburn. The longevity of her career I think is inspiring to everyone," said Blanchett. She added thanks to Scorsese, saying: "I hope my son will marry your daughter."
Best foreign film
The Sea Inside (Spain), directed by Alejandro Amenabar, won as best foreign-language film. It told the real-life story of a paralysed Spaniard, played by Javier Bardem, who fought a legal battle for his right to die.
Born Into Brothels, which examines the lives of children of prostitutes in Calcutta, India, received the Oscar for feature-length documentary.
The Oscar for best original song went to Al Otro Lado Del Rio from The Motorcycle Diaries, which was the first Spanish-language song ever to be nominated.
The Sea Inside won the best
foreign-language film prize
The superhero action comedy The Incredibles won the animated-feature prize, beating 2004's biggest box-office hit, the fairy-tale sequel Shrek 2.
"I don't know what's more frightening, being watched by millions of people, or the hundreds of people that are going to be annoyed with me tomorrow for not mentioning them," said Brad Bird, writer-director of the The Incredibles.
The first prize of the night, for art direction, went to The Aviator, whose awards included cinematography, film editing and costume design.
Eternal Sunshine of the Spotless Mind took the original-screenplay award for Charlie Kaufman. Sideways won the adapted-screenplay prize for director Alexander Payne and his writing partner, Jim Taylor.
"My mother taught me to write, and she died before she could see any of this, so this is for you, mom," Taylor said.