The Globe win could boost Mo'Nique's prospects at the Oscars, whose nominations come out Feb. 2.
"Precious" also was up for best drama, along with the sci-fi blockbuster "Avatar," the recession tale "Up in the Air" and the war stories "The Hurt Locker" and "Inglourious Basterds."
Rain doused the pre-show, stars in their finery crowding under umbrellas as storms rolled in.