By Brandon Griggs, CNN

(CNN) -- It was supposed to be "A Star is Born's" night. Instead, top honors went to another popular movie about the unlikely rise of a powerhouse singer.

In an upset, "Bohemian Rhapsody," the biopic about Freddie Mercury and British rock band Queen, won best drama at the 76th annual Golden Globes on Sunday. Rami Malek, who won raves for his full-throated portrayal of the late Mercury, won best actor in a drama and thanked Mercury onstage "for giving me the thrill of a lifetime."

"Green Book," the inspirational true story about a budding friendship between an African-American pianist and a white bouncer on a tour of the Deep South in the early 1960s, won three Globes, including best picture in the musical/comedy category. It beat out "Vice," the polarizing Dick Cheney biopic, which led all films with six nominations.

"Green Book's" director, Peter Farrelly, made a plea for tolerance in his acceptance speech. "We are still living in divided times, maybe more so now than ever," he said. "All we have to do is just talk and not judge people by their differences, and look for what we have in common."

Bradley Cooper's acclaimed remake of "A Star Is Born," which was widely expected to win several top prizes, took only one award, for best song -- its centerpiece hit, "Shallow."

"Bohemian Rhapsody" has been a worldwide box-office smash but has received mostly lukewarm reviews from critics and weathered some controversy -- its original director, Bryan Singer, was reportedly fired before filming was completed. Its Golden Globe success may boost its chances for Oscar nominations, to be announced January 22.

The Globes honor the year's best in movies and TV and are voted on by the 90 or so members of the Hollywood Foreign Press Association, whose choices are often quirkier than those of the Academy of Motion Picture Arts and Sciences. But as the first awards show of the season, the Globes have an outsized influence on Academy Award predictions -- and voting on Oscar nominees begins Monday.

The Globes always split the best-picture nominees into two categories: drama and musical/comedy. That made for some head-scratching this year when two movies about music, "A Star is Born" and "Bohemian Rhapsody," were nominated as dramas.

Sunday's awards were spread far and wide, with few movies or TV series winning more than once. But the show had its share of surprises.

The TV awards

"The Americans," the FX series about Russian spies posing as a married couple in suburban Washington, won best TV drama. The critically praised show, which just wrapped its sixth and final season, stars real-life couple Keri Russell and Matthew Rhys.

But Rhys lost the award for best actor in a TV drama to Richard Madden, who won for his role as a British security officer in the BBC/Netflix political thriller "Bodyguard."

"The Americans" beat out "Homecoming," the new Julia Roberts show about a counselor at a mysterious treatment center for returning veterans, and "Killing Eve," about the treacherous rivalry between two dangerous women, a British intelligence officer and an assassin. But "Eve's" Sandra Oh -- who also co-hosted the Globes with Andy Samberg -- won for best actress in a TV drama.

"I have no idea what is happening," she said, looking stunned (or maybe just mock-stunned) upon returning to her hosting duties, her Golden Globe still in her hand.

In a mild surprise, best comedy series went to Netflix's "The Kominsky Method," starring Michael Douglas as an aging thespian who runs a prestigious acting class. Douglas also won the award for best actor in a TV comedy.

For the second year in a row, Rachel Brosnahan won best actress in a comedy for "The Marvelous Mrs. Maisel," the Amazon series about a 1950s housewife in New York City who finds she has a gift for stand-up comedy.

"The Assassination of Gianni Versace: American Crime Story" won two awards: Best TV movie or limited series, and Darren Criss for best actor.

With the exception of "Mrs. Maisel," none of last year's TV nominees were nominated again this time around -- partly because hits like "Game of Thrones" and "Master of None" didn't air new episodes in 2018.

The other big movie awards

In another upset, Glenn Close won best actress in a drama for her role as a long-suffering spouse in "The Wife." Lady Gaga, whose soulful performance anchored "A Star Is Born," had been considered the favorite.

In an emotional speech, Close said that women in Hollywood should not be afraid to stand up for their careers. "We have to find personal fulfillment," she said. "We have to say, "I can do that. And I should be allowed to do that.' "

Shape-shifting actor Christian Bale, who famously gained 40 pounds to play former Vice President Dick Cheney, won best actor in a comedy for "Vice." "Thank you to Satan for giving me the inspiration on how to play this role," he joked.

Olivia Colman won best actress in a comedy for her performance as daffy Queen Anne in "The Favourite."

"Green Book," arguably the night's biggest winner, also took best screenplay and best supporting actor for Mahershala Ali.

Also receiving multiple awards was "Roma," Alfonso Cuaron's affectionate look at his childhood in Mexico City, which won for best foreign film and best director. The film has received rapturous reviews but is already streaming on Netflix and is only playing in a few theaters, which could hurt its Oscar chances.

The moments

The show's hosts, Oh and Samberg, mostly avoided politics in their opening comments. There was no mention of President Trump or the government shutdown, although the pair made jokes about identity politics and cultural appropriation. They also alluded to the (as of now) host-less Academy Awards, joking about holding a contest in which "one lucky audience member will host the Oscars."

But some of their comic bits felt flat, including a gag about Jim Carrey being in the wrong seat and a bit in which fake doctors swarmed the room to administer "flu shots," which left many stars looking confused.

Jeff Bridges, one of the most beloved actors in Hollywood, received the Cecil B. DeMille Award for his lifetime of work in such films as "The Last Picture Show," "Starman," "The Big Lebowski" and "True Grit."

During his acceptance speech he thanked his late father, Lloyd Bridges, and pulled up his sleeve to reveal his dad's cuff links. "They were your dad's, too!" he said, before launching into a rambling metaphor about steering ships.

One of the night's more poignant moments came when Steve Carell presented a new award to TV legend Carol Burnett. The annual award will be named for the 85-year-old comic actress, who gave a heartfelt speech about how TV networks would never produce a variety show like hers today because they cost too much money.

"So here's to reruns and YouTube," she said. "I'm just happy our show happened when it did." Burnett finished with her trademark tug on her ear and left the stage to a standing ovation.