The gala at the Beverly Hilton also recognized Alfonso Cuaron's "Roma", a cinematic ode to his childhood in 1970s Mexico City, with best director and foreign film honors, while seven movies bagged one statuette each. In fact, he said that many actors and "big names" approached him at the awards and fangirled a bit.
The actor paid tribute to the late singer in his acceptance speech, as well as thanking Queen guitarist Brian May and drummer Roger Taylor - both of whom attended the ceremony.
Referring to the current Republican Senate majority leader, he added: "What do you think?"
Green Book won three gongs, Motion Picture - Musical or Comedy, Best Screenplay and Best Actor in a Supporting Role in any Motion Picture for Mahershala Ali.
The EE British Academy Film Awards will take place on February 10 at London's Royal Albert Hall.
Check out Malek's speech below, and see the full list of Golden Globes winners here.
In contrast to the political barbs, often directed at U.S. President Donald Trump, that have marked recent awards shows, Sunday's Golden Globes had a more positive vibe.
Sandra Oh won best actress in a TV drama for Killing Eve, the unconventional crime drama that started out on BBC America.