"This is for Hal. You're always in my heart," Janney, 58, said.
Hal's battles influenced Janney to take on the role of Bonnie Plunkett, a recovering addict, in "Mom."
"I was around the world of recovery a lot, trying to get my brother to want to recover," Janney told CBS News in 2016.
"He didn't," she continued. "He lost his battle with addiction and other things. And I felt like this was important for me to take a part like this and be a part of a show that showed people in recovery, and also showed that there was hope."
During her acceptance speech Sunday night, Janney also thanked her "'I, Tonya' family...that elevated my work."
She also thanked fellow actress, Joanne Woodward "for your encouragement and generosity that gave me the confidence to think I could pursue a career in acting."