The Misery star wasn't close to Williams, but she has fond memories of their few run-ins during previous awards shows, when he had always shown her nothing but love.
Recalling her very first encounter with the Good Will Hunting Oscar winner back in 1991, Bates says, "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 remembers how Williams was looking out for her again in 1999, when she lost out to Judi Dench for the Best Actress in a Supporting Role accolade, an Oscar the funnyman was on hand to present.
She tells The Hollywood Reporter, "He came to me and said, 'I really wished I could have had your name in the envelope; are you Ok? I know how hard it is to lose.' He was so kind to me."
And Bates reveals she had Williams on her mind as she stepped up onstage at Monday's Los Angeles ceremony to collect her gong for Outstanding Supporting Actress in a Mini Series or Movie for her role in American Horror Story: Coven.
She says, "I almost wanted to say, 'Look, I won this time and this is for you,' but I was just so... nervous."
The Primetime Emmy Awards included a special In Memoriam tribute to Williams from his close friend and fellow funnyman Billy Crystal.