Davis completed her collection by winning best audio book for her autobiography Finding Me.
“I wrote this book to honour the six-year-old Viola,” said the star. “To honour her life, her joy, her trauma, everything.”
The star won the best supporting actress Oscar in 2016 for Fences.
Her Emmy Award recognised the TV drama How To Get Away With Murder, and she has two Tony Awards for her theatre work – featured actress in a play for King Hedley II (2001) and lead actress in a play for Fences (2010).
“I just EGOT!” announced the star on stage at the Grammys, becoming visibly emotional as she thanked her family for being “the best chapter in my book”.
The 17 other EGOT winners include Sir John Gielgud, Rita Moreno, Andrew Lloyd Webber, John Legend and Jennifer Hudson.
The premiere ceremony was hosted by YouTube star Randy Rainbow, who went viral during the Trump administration for videos that mixed political commentary with musical theatre numbers.
Taking to the stage at Los Angeles’ Crypto,com Arena, he promised not to make cheap jokes about US Republican George Santos, who has admitted to making several false statements in his resume and biography.
“I will not even say his name,” said Rainbow. “Even though he is nominated for best pop vocal album.”