The emotionally fragile actress won two Tonys, an Emmy and an Oscar as well as multiple nominations in all three, the New York Times reported Monday.
The stress of the show -- which ran for 300 performances on Broadway then toured for six months -- set Stapleton on a path of alcoholism and paranoia, which she battled throughout her career, the newspaper said.
She went on to star in several Williams' plays through the years as well as make her mark on both the big screen and TV.
She won her Emmy in 1967 for "Among the Paths to Eden," a Truman Capote story about a spinster and a widower.
Her second Tony was for Neil Simon's "The Gingerbread Lady" in 1970 and she won her Oscar for best supporting actress in the 1981 film "Reds."
Among her other screen roles were parts in "Bye Bye Birdie," "Miss Lonelyhearts," "Interiors," "Airport" and "Cocoon."
Twice-divorced, Stapleton is survived by a son, a daughter and a brother.