The 25-year-old, who was absent from this year’s ceremony due to a dispute with the show’s producers, won Best Pop Vocal Album for Sweetner.
She thanked fans for the win in a black and white video of herself tucked up in bed with pet dog, Myron. She adopted him from Miller, who died of an accidental overdose in 2018.
Snuggled up with her eyes closed she said: “Is it rolling? Thank you so much.”
She captioned the post: “It’s me your tiny, highly emotional, Italian, and now Grammy award winning friend. I’m super tarnished lol. But super grateful. Thank u for everything. Myron is in my arms n he says hi as well.”
She shared a string of congratulatory messages from fans on her Instagram stories, including one from American actress Elizabeth Gillies who wrote: “So proud of you, MY DINGUS!!!”
Grande beat off competition from Camila Cabello, Kelly Clarkson, Shawn Mendes, Pink and Taylor Swift for her comeback album Reputation to take the title.
She apologised to fans for not attending Sunday night’s ceremony in Los Angeles after previously taking issue at her “creativity & self-expression” being “stifled”.
“F***,” she wrote before adding: “I know I’m not there tonight (trust, I tried and still truly wished it had worked out tbh) and I know I said I try not to put too much weight into these things .... but f*** ....... this is wild and beautiful. Thank you so much.”
Grande defended herself against Grammys organiser Ken Ehrlich after he claimed the thank u, next singer could not “pull something together” last-minute for the show.
She tweeted: “I can pull together a performance over night and you know that, Ken.
“I offered 3 different songs. It’s about collaboration. It’s about feeling supported. It’s about art and honesty. Not politics. Not doing favours or playing games. It’s just a game y'all.. and I’m sorry but that’s not what music is to me.”