The supporting-actor prize Sunday went to Christopher Plummer as an elderly widower who comes out as gay in the father-son drama "Beginners."
Williams offered thanks for giving her the same award Monroe once won and joked that her young daughter put up with bedtime stories for six months spoken in Monroe's voice.
"I consider myself a mother first and an actress second, so the person I most want to thank is my daughter, my little girl, whose bravery and exuberance is the example I take with me in my work and my life," Williams said.
The black-and-white silent film "The Artist," which led the Globes with six nominations, split its first two awards of the evening, winning the musical-score prize for composer Ludovic Bource but losing out on best screenplay for director-writer Michel Hazanavicius.
Woody Allen won the screenplay honor for his romantic fantasy "Midnight in Paris," the filmmaker's biggest hit in decades. Never a fan of movie awards, Allen was a no-show at the Globes, where he previously won the screenplay honor for 1985's "The Purple Rose of Cairo.
The wins boost Williams and Plummer's prospects for slots at next month's Academy Awards, whose nominations come out Jan. 24.
The Oscars are an honor for which Monroe herself never was nominated, though she was a two-time nominee at the Globes and won for best actress in a musical or comedy for 1959's "Some Like It Hot."
In "My Week with Marilyn," Williams plays Monroe as an insecure performer struggling to establish herself as a genuine actress rather than a movie star sexpot just a couple of years before "Some Like It Hot." The film chronicles Monroe's contentious time shooting the 1957 romance "The Prince and the Showgirl" alongside exasperated director and co-star Laurence Olivier.
Like Monroe, Oscar consideration has been elusive for the 82-year-old Plummer, who has been nominated for Hollywood's top honor only once in his 60-year career - two years ago, for the Leo Tolstoy drama "The Last Station."
"I must praise my distinguished competitors, who whom I have the greatest admiration and to whom I apologize most profusely," said Plummer, who added warm regards to "Beginners" star and Scottish actor Ewan McGregor. "I want to salute my partner, Ewan, that wily Scot, Ewan 'My Heart's in the Highlands' McGregor, that scene-stealing swine from the outer Hebrides."
Plummer is regarded as one of the finest Shakespearean stage actors of the last half century. His film roles range from Austrian widower Captain von Trapp in "The Sound of Music" and Tolstoy in "The Last Station" to newsman Mike Wallace in "The Insider" and a treacherous Klingon general in "Star Trek: The Undiscovered Country." He also co-starred in the current thriller "The Girl with the Dragon Tattoo."
The prize for best animated film went to Steven Spielberg's action tale "The Adventures of Tintin," a Paramount-Sony co-production that dealt the first Globes loss to Disney unit Pixar Animation. Pixar films such as "Ratatouille," ''WALL-E" and "Toy Story 3" had won all five previous times since the Globes added the category.
Spielberg thanked his producing partner on the film, "The Lord of the Rings" creator Peter Jackson, along with both studios behind the film, based on what the director pointed out was a series of picture books by Belgian writer Herge that started 80 years ago.
"I would like to thank two studios that really proved the adage that Peter and I could make the telephone book if we wanted to," said Spielberg, whose World War I epic "War Horse" is nominated for best drama.
The Iranian drama "A Separation" was chosen as best foreign-language film. Writer-director Asghar Farhadi uses a divorcing couple's domestic troubles with a young child and an aging parent as the means to examine gender, religious and class distinctions in contemporary Iran.
Ricky Gervais, who has ruffled feathers at past shows with sharp wisecracks aimed at Hollywood's elite and the Globes show itself, returned as host for the third-straight year. He started with some slams at the Globes as Hollywood's second-biggest film ceremony, after the Oscars.
Gervais joked that the Globes "are just like the Oscars, but without all that esteem. The Globes are to the Oscars what Kim Kardashian is to Kate Middleton. A bit louder, a bit trashier, a bit drunker and more easily bought. Allegedly. Nothing's been proved." He also needled early winners, saying the show was running long and stars needed to keep their speeches short.
"You don't need to thank everyone you've ever met or members of your family, who have done nothing," Gervais said. "Just the main two. Your agent and God."
After winning for musical score, "The Artist" composer Bource apologized for his halting English, saying, "I'm sorry, I'm French," adding that he's better with music than words.
"Right now, if I were to write a song, it would be a tap-dance number," Bource said. "The power of music is at least universal. The gift of the silent film is that it is so universal."
Madonna, Julie Frost and Jimmy Harry won the Globe for best song for "Masterpiece" from the King Edward-Wallis Simpson drama "W.E.", which Madonna also directed.
Among television winners were Kate Winslet as best actress in a miniseries or movie in "Mildred Pierce,"Idris Elba as best actor in a miniseries or movie in "Luther," Laura Dern as comedy or musical actress in "Enlightened," Kelsey Grammer as dramatic actor in "Boss," ''Homeland" for drama series and "Downton Abbey" for miniseries or movie.
A drama with comic touches, "Beginners" was a fitting recipient to start the Globe ceremony, which has a strong lineup of lighter fare to match the more sober-minded films that generally dominate Hollywood awards.
Alongside those heavyweight dramas, the category for best musical or comedy at the Globes usually is more of a lark, with nominees rarely emerging with best-picture prospects at the Academy Awards.
Yet Sunday's musical or comedy contenders made up a strong bunch that could give their best-drama cousins at the Globes a run for their money come Oscar time.
Among the six nominations for "The Artist" were best musical or comedy, director for Hazanavicius, and acting slots for Jean Dujardin and Berenice Bejo.
Tied for second with five nominations each are the Deep South tale "The Help" and George Clooney's Hawaiian family story "The Descendants," both of them among best-drama contenders.
With the Oscars choosing up to 10 best-picture contenders when nominations come out Jan. 24, "The Artist" could have some other comic company there. Globe musical or comedy nominees "Midnight in Paris" and "Bridesmaids" also have solid Oscar nomination prospects.
Most years, the musical or comedy category is filled with nominees that have little or no chance at the Oscars, such as last year's Globe nominees "The Tourist" and "Burlesque." The last time a musical or comedy Globe winner earned the best-picture Oscar was nine years ago, when "Chicago" triumphed at both shows.
This time, the dual categories at the Globes could create an Oscar showdown between the dramatic and musical-comedy winners.
Along with "The Artist," Kristen Wiig's wedding romp "Bridesmaids" and Woody Allen's romantic fantasy "Midnight in Paris," Globe nominees for best musical or comedy are Joseph Gordon-Levitt's cancer tale "50/50" and Michelle Williams' Marilyn Monroe story "My Week with Marilyn."
Besides "The Descendants, "The Help" and "War Horse," best-drama contenders are Martin Scorsese's Paris adventure "Hugo," Clooney's political thriller "The Ides of March" and Brad Pitt's sports tale "Moneyball."
Presented by the Hollywood Foreign Press Association, a group of 89 entertainment reporters for overseas outlets, the Globes used to have a strong record predicting the films that would go on to win best-picture at the Oscars. But lately, a best-picture win at the Globes has not translated into victory on Oscar night.
Over the last seven years, only one Globe best-picture winner - 2008's "Slumdog Millionaire" - has gone on to claim the top Oscar trophy. Before that stretch, the Globes had been on an eight-year streak in which one of its two best-picture recipients also won the main prize at the Academy Awards.
Last year, "The Social Network" won best-drama at the Globes and looked like the early Oscar favorite. But momentum later swung to eventual Oscar best-picture winner "The King's Speech." The year before, "Avatar" was named best drama at the Globes, while "The Hurt Locker" took best picture at the Oscars.
The Globes have a better track record predicting who will win Oscars for acting. A year ago, all four actors who won Oscars earned Globes first - lead players Colin Firth for "The King's Speech" and Natalie Portman for "Black Swan" and "The Fighter" supporting stars Christian Bale and Melissa Leo.