Bates, 66, received the honor for her role in FX's American Horror Story: Coven decided to dedicate the award to the cast and crew of the Ryan Murphy show, but she revealed backstage that she originally meant to dedicate it to the late actor.
"When I won my first major award for Misery -- a Golden Globe -- they didn't have cell phones and I was waiting at a pay phone to call my mother afterward and I didn't have a quarter. I turned around and asked, and Robin said, 'Here's a quarter to call your mother.' I never forgot that kindness," the actress said after Billy Crystal's tribute for Williams.
Bates also reminisced about a time she was nominated for an Academy Award in 1988, but lost to Judy Dench. Williams, a winner that night for Good Will Hunting, was the one who presented the award.
"He came to me on the commercial break and said, 'I really wish I could have read your name. Are you okay? I know what it's like to lose.'"
After admitting she didn't know the actor that well, Bates explained Monday's win was "special" for that reason and she wanted to share it with him.
"I almost wanted to say, 'Look, I own this time and this is for you,' but I was just so ... nervous."