BEVERLY HILLS, Calif. — The Golden Globes are typically Hollywood’s bawdiest awards show — “a wonderful mess,” said co-host Tina Fey of this year’s bash. But in the end, after all the boozy banter — some of it bleeped for broadcast — the 1970s corruption tale “American Hustle” got a very serious push toward Oscar glory, picking up three major awards.

Benefiting the most from Sunday night’s Globes as focus shifts to the Academy Awards, David O. Russell’s con caper locked in best comedy, best actress (Amy Adams) and best supporting actress (Jennifer Lawrence).

Not that early-season favorite “12 Years a Slave” isn’t still in the running. Though it earned only one award, Steve McQueen’s historical epic took home the night’s top honor: best film drama. But “American Hustle” seems to have emerged from the 71st annual Golden Globes as the film to beat.

Oscar doesn’t usually care much for comedies, but “American Hustle” offers a rich blend of scandal, style and superb acting that is bound to get Academy voters’ attention.

The Globes have flipped awards season momentum before. Though Ben Affleck was denied an Oscar nomination last year for directing “Argo,” he did win best director at the Globes and his film went on to win best picture at the Oscars. In 2009, Katherine Bigelow’s “The Hurt Locker” lost in the best film category to James Cameron’s “Avatar” at the Globes. The defeat seemed to sway Oscar voters in Bigelow’s favor and she snagged the best picture award.

With the Oscar nominations coming Thursday, lost-in-space saga “Gravity,” which earned Alfonso Cuaron the best director Globe, could pick up some additional pull with likely nominations in the craft categories, which theGlobes don’t recognize. There’s also a lot of built-in affection for its leading lady, Sandra Bullock, not to mention the film’s impressive worldwide box office performance.

Hosting Sunday night’s Globes for the second year in a row, Fey and Amy Poehler drew big laughs as they targeted such A-listers as Matt Damon, Meryl Streep and Leonardo DiCaprio.

One of the evening’s well-received jokes was delivered in the “SNL” alums’ opening bit in a reference Fey made to “Gravity”: “It’s a story of how George Clooney would rather float away into space and die than spend one more minute with a woman his own age.”

Last year, the duo led a six-year ratings high with 19.7 million viewers. They’ll return as hosts next year.

Besides “American Hustle” and “12 Years a Slave,” the Hollywood Foreign Press Association, which presents theGlobes, also favored other fact-based films from America’s past: the ‘80s-era AIDS drama “Dallas Buyers Club” and the high-finance extravaganza “The Wolf of Wall Street,” which both won top awards.

“Dallas Buyers Club” stars Matthew McConaughey and Jared Leto, who both lost noticeable weight for their roles — “or as actresses call it, ‘being in a movie,’” joked Fey — won their first Globes for best dramatic actor and best supporting actor. DiCaprio, a nine-time nominee, picked up his second Globe for best comedy actor for his turn as a provocative stockbroker in Martin Scorsese’s nearly three-hour “Wall Street.”