Vincente Minnelli, whose deft intermingling of song, dance and plot made him one of the greatest directors of Hollywood musicals, died in his sleep at his home in Los Angeles last night. He was 76 years old. The director had been hospitalized several times within the last year for emphysema and pneumonia, according to Ron Wise of the Cedars-Sinai Medical Center.

Mr. Minnelli won an Academy Award for directing ''Gigi'' in 1958. The prize was one of nine Oscars for the picture, the most any movie had won until then. Among the other Oscars for ''Gigi'' was the one for best film of the year, which Mr. Minnelli's 1951 movie ''An American in Paris'' also received.

The director's other notable film musicals included ''The Band Wagon'' (1953), ''Meet Me in St. Louis'' (1944) and ''The Pirate'' (1948).

The latter two starred the tempestuous singer-actress Judy Garland, to whom he was married from 1945 to 1951. Their daughter, Liza, inherited Mr. Minnelli's large dark eyes and Miss Garland's stage talents and won an Academy Award herself, for her performance in ''Cabaret'' (1972).

''How many men,'' Mr. Minnelli asked proudly in his 1974 autobiography, ''can lay claim to being loved by the most extraordinary talents of not one, but two generations? And who loved, not always wisely, in return? But love is what life is all about. Love of wife, love of family, love of work.''

Besides musicals, Mr. Minnelli's three dozen movies also included successful serious films, such as ''The Bad and the Beautiful'' (1952) and ''Lust for Life'' (1956), and comedies that did not rely on music, such as ''Father of the Bride'' (1950). Joked About Epitaph

''Basically,'' Mr. Minnelli wrote in the autobiography, ''I Remember It Well,'' ''I work to please myself. I'm still not sure if movies are an art form. And if they're not, then let them inscribe on my tombstone what they could about any craftsman who loves his job: 'Here lies Vincente Minnelli. He died of hard work.' ''

Elegant and suave, but high-strung, Mr. Minnelli did work hard, painting signs as a schoolboy, designing show-window displays, then gaining recognition as a designer of theatrical scenery and costumes. He began as a director with three successful Broadway shows, ''At Home Abroad'' (1935), ''The Show Is On'' (1936) and ''Hooray for What!'' (1937).

Inevitably, he was summoned to Hollywood, and in 1940 he began his 26 years with the Metro-Goldwyn-Mayer studio. It was his good fortune to be in the right place at the right time: the 1940's and 1950's were the heyday of the color movie musical.

Once in Hollywood, Mr. Minnelli quickly became an acknowledged master of the form. He had a superb sense of proportion and balance, his admirers said, in addition to his ability to create an aura of sophistication and a tone of nostalgia without going overboard. Color and Character

And his use of color won perennial praise. Reviewing ''Lust for Life,'' a screen biography of the painter Vincent van Gogh that starred Kirk Douglas, the New York Times critic Bosley Crowther wrote that Mr. Minnelli had ''wisely relied on color and the richness and character it gives to images.''

''The cold grayness of a mining district,'' Mr. Crowther wrote, ''the reds of a Paris cafe, the greens of a Provencal village or the golden yellows of a field of ripening grain - these give us a sensory knowledge of the surroundings that weigh upon van Gogh.''

Appraisals of Mr. Minnelli's work have varied. The playwright and lyricist Alan Jay Lerner (who died on June 14), wrote in 1974 after several collaborations with him that Mr. Minnelli was ''the greatest director of motion picture musicals the screen has ever known.''

''His best was the best there ever was.''

But Mr. Minnelli also came in for some critical jabs and buffetings, especially late in his career. The critic Andrew Sarris once wrote bluntly, ''Minnelli believes more in beauty than in art.'' Mr. Crowther said Mr. Minnelli had directed the gaudy 1955 musical ''Kismet'' as though implementing ''marching orders for the Macy parade.'' Liked Sweeping Canvases

As a director, Mr. Minnelli liked to work on sweeping canvases. He made much use of dreams and of dreamlike, ethereal atmospheres, and of settings that were remote in space or time, such as the Paris of ''An American in Paris'' or the turn-of-the-century America of ''Meet Me in St. Louis.''

He used dance skillfully and lavishly in his films. The 17-minute climactic dream ballet in ''An American in Paris,'' danced by Gene Kelly and Leslie Caron, was said by the French-born film scholar Jean-Pierre Coursodon, writing three decades later, to be ''unquestionably the greatest set piece in the entire history of the film musical.''

Mr. Minnelli elicited some fine performances from his actors and actresses, varying his directing technique as the occasion required.

''I feel there are no rules,'' was how he once put it. ''The minute you make a rule, you're dead. It's the matter of the moment, and how you put it. There's always a key word that gives the actor the point of view that you want.'' Made Budding Talents Bloom

Reviewing ''The Clock,'' released in 1945, Time magazine said, ''Vincente Minnelli's talents are so many-sided and generous that he turns even the most over-contrived romanticism into something memorable. He has brought the budding dramatic talents of his betrothed, Judy Garland, into unmistakable bloom.''

Yet Miss Garland herself had mixed feelings about the way he directed her. Shortly before their marriage, she said in an interview, ''Vincente is such a wonderful director, but he gets excited and stutters and doesn't finish his sentences - just says, 'Well, you know what I mean.' ''

For a time after their wedding, Mr. Minnelli recalled in his memoirs, their life together was ''atypically golden, even for Hollywood.''

''Judy and I weren't falling prey to the Hollywood syndrome where one mate is up and the other is down,'' he wrote.

But he added that later in their marriage, she suffered intermittently from emotional problems and addiction to barbiturates and benzedrine, and her work as an actress suffered. Breakup of Marriage

In June 1950, M-G-M suspended her contract and, Mr. Minnelli reported, an attorney for the studio said, ''Miss Garland's inability to get into wardrobe and makeup on time has added at least 20 percent to the cost of her pictures.''

Ten days later, Mr. Minnelli wrote, she locked herself in a bathroom at home and began to scream, ''Leave me alone! I want to die!''

After apparently cutting herself with a broken glass, Miss Garland was taken to a doctor. ''He looked at the injury,'' Mr. Minelli wrote. '' 'It's only a scratch,' he said. 'But all suicide attempts are desperate cries for help. You must realize that.' We, of course, did.'' But to escape the pains of his marriage, Mr. Minnelli threw himself into his work. In February 1951, Miss Garland filed for divorce in Los Angeles, charging cruelty, and in March she divorced him, testifying that he ''secluded himself and wouldn't explain why he would be away and leave me alone so much.'' Show-Business Family

Yet working hard and long at show business was something of a tradition in Mr. Minnelli's own family. His Italian-born father, a musician, and an uncle operated the Minnelli Brothers Tent Theater, which toured small towns in Ohio, Illinois and Indiana; his French-born mother acted in the plays.

She gave birth to Vincente on Feb. 28, 1910, in Chicago and he, too, appeared in the family's productions as a small boy. Later, after graduating from high school in Delaware, Ohio, he went to work as an apprentice show-window-display designer at the Marshall Field department store in Chicago.

There, he also attended the Art Institute of Chicago for a time and became a costume designer for the Balaban & Katz movie theater chain, which also put on stage shows.

Then Mr. Minnelli moved to New York, where he did various kinds of theatrical design work. Before long he was asked by Grace Moore, the singer and actress, to do the settings and costumes for the 1932 production of the operetta ''DuBarry,'' in which she played the title role. Broadway to Hollywood

After going on to achieve success as a Broadway director, Mr. Minnelli was brought to Hollywood by the Metro-Goldwyn-Mayer producer Arthur Freed, who was to produce all the musicals Mr. Minnelli directed for the studio.

During his M-G-M years, as Alan Jay Lerner later recalled good-humoredly, the director, as seen by his studio colleagues, was ''a man of average height, slender, his dark hair brushed tightly against his head, his mouth twitching and his large, black, soft eyes in a chronic state of pop.''

Mr. Minnelli fulfilled his longstanding ambition to direct Liza Minnelli when she starred in his 1976 film ''A Matter of Time.'' Vincent Canby wrote in The Times that it had ''moments of real visual beauty,'' although ''what the characters say to each other is mostly dumb.''

In April 1986, Mr. Minnelli was awarded the Legion of Honor by the French Government.

Mr. Minnelli's second marriage, to Georgette Magnani in 1954, ended in divorce in 1958. His third marriage, to Denise Gigante in 1960, also ended in divorce, in 1971.

He is survived, in addition to his wife, Lee, and his daughter Liza, by Christiana Nina Minnelli, a daughter from his second marriage.

Photo of Vincente Minnelli with daughter Liza in 1983 (AP)

Lester Anthony Minnelli