Correction Appended

LOS ANGELES, March 24— ''A Beautiful Mind'' won the Oscar for best picture of 2001 in ceremonies tonight in Hollywood that also included the first Oscar for a black actor in a lead role in almost four decades and the first for a black actress in a lead role in Academy Award history.

''A Beautiful Mind,'' a romantic drama about a Princeton University mathematician who overcame schizophrenia and won a Nobel Prize also took awards for Ron Howard's direction, Jennifer Connelly's supporting performance and Akiva Goldsman's script. Although beset in recent weeks by charges about liberties taken in telling the story of the Nobel laureate John Forbes Nash Jr., ''A Beautiful Mind'' nevertheless managed to dominate the 74th annual awards ceremonies. Mr. Nash was in the audience.

It was also a momentous night for black actors in Hollywood, with wins for Denzel Washington and Halle Berry, an honorary Oscar to Sidney Poitier, the black actor who last won the lead Oscar for ''Lilies of the Field'' (1963) and a black M.C., Whoopi Goldberg.

Mr. Washington, who won for his portrayal of a corrupt police officer in ''Training Day,'' had previously won a supporting Oscar for ''Glory'' (1989). ''I think it's more exciting or surreal the first time,'' Mr. Washington said backstage. ''I was just with Halle, and she's just gone. She doesn't know where she is.''

''Forty years I've been chasing Sidney and what do they do?'' Mr. Washington said. ''They give it to him again on the same night. I'll always be chasing you Sidney. I'll always be following in your footsteps. There's nothing I'd rather do.''

In the evening's most emotional moment, a stunned Halle Berry walked shaking to the microphone to accept her Oscar for best lead actress in ''Monster's Ball,'' in which she played the wife of a black convict who forges a relationship with a white prison guard. Ms. Berry struggled through tears to thank the black actresses who came before her and those who are working today.

''The door has been opened,'' she said, holding the Oscar aloft.

Jim Broadbent won best supporting actor as the husband of the British author Iris Murdoch, who suffered from Alzheimer's disease, in ''Iris.''

Julian Fellowes, a British actor-turned-writer, won the original screenplay Oscar for his first produced script, ''Gosford Park,'' a British murder mystery from the director Robert Altman. ''I think you must be the most generous nation on earth,'' he told the largely American audience.

Best makeup went to ''The Lord of the Rings: The Fellowship of the Ring,'' which also won for its visual effects, for Andrew Lesnie's cinematography and for Howard Shore's score. ''Pearl Harbor'' got the award for sound effects editing. Best costume design and best art direction went to ''Moulin Rouge,'' while ''Black Hawk Down'' won for its sound and editing.

And for the first time, an Oscar was presented to the best animated feature film, and it went to ''Shrek,'' a computer-animated family comedy about an ogre, a mule and a princess. But the chief competitor of ''Shrek,'' the computer-animated ''Monsters, Inc.,'' did not leave empty-handed. Randy Newman, the composer and songwriter who had been nominated for 16 Oscars over the years, won his first one for ''If I Didn't Have You,'' a song from ''Monsters.'' ''I would like first to thank the music branch for giving me so many chances to be humiliated over the years,'' Mr. Newman said.

Tonight's ceremony culminated one of the longest, most expensive and, many believe, mean-spirited Oscar campaigns in recent memory. There were jokes to relieve the tension. In a year in which three black actors were nominated for leading roles for the first time in three decades, the evening's M.C., Whoopi Goldberg, said, ''So much mud was thrown this year, all the nominees were black.''

The Oscars were presented amid some of the tightest security the ceremony has ever had, spurred not only by worries stemming from Sept. 11 but by the event's difficult new home, the Kodak Theater, in one of the most densely populated neighborhoods in Los Angeles.

''Security here tonight is tighter than some of the faces,'' Ms. Goldberg said.

A burgundy carpet spread across Hollywood Boulevard under glowering, late afternoon skies that occasionally unleashed a spattering of chilly raindrops on the crowd below. Some 400 fans who had applied for seats in the bleachers, and passed a security background check, cheered from beneath a line of giant outdoor television screens flanked by monolithic Oscar statues.

Across the country, another giant outdoor screen was showing the ceremony live in Times Square.

Inside the recently opened Kodak Theater were more than 3,100 nominees, presenters and guests. The theater was designed to look stunning on television and to keep even those in the uppermost seats as close as possible to the stage.

Sidney Poitier said he accepted his honorary Oscar ''in memory of all of the African-American actors who went before me, on whose shoulders I stand.'' And he paid special tribute to the white producers and directors who had helped him break the color barrier for Hollywood leading men.

In accepting his honorary Oscar, Robert Redford urged Hollywood studios to fight the urge to play it safe. ''Make sure we embrace the risks as well as the sure things,'' he said.