"I wanna thank my wife Catherine for her support," the 68-year-old actor said onstage at the annual awards show.
Douglas also got a few big laughs from the audience while thanking Matt Damon, who played Liberace's longtime love in the well-received HBO film.
"This was a two-hander, and Matt, you're only as good as your other hand," he said.
"You were magnificent and the only reason I'm standing here is because of you," he added. "So you really deserve half of this [award]. Do you want the bottom or the top?"
Here's video of his speech:
Douglas told reporters backstage that "two-hander" is a common acting term to describe how one actor is only as good as his or her partner.
"We relied on each other through this whole experience, and I wouldn't be up onstage without Matt and his performance and his commitment," he said.