The cause of Conway's death was not publicized, but he reportedly suffered complications from Normal Pressure Hydrocephalus without signs of dementia or Alzheimer's.
Conway won three Emmy awards for acting on the Burnett show and a fourth as a writer in the 1960s and '70s. He won two more Emmys for guest appearances on Coach and 30 Rock.
Conway also had a modest but steady movie career, appearing in such films as "The Apple Dumpling Gang" (1975), "The Shaggy D.A".
Burnett and her co-horts-Conway, Vicki Lawrence, and Jim Nabors wearing a shirt that is so gay it makes Charles Nelson Reilly look like Jimmy Carter-emerge from the black void beyond the studio cameras and immediately steal focus from host Gene Rayburn.
"If there's any reason at all I'm in the business, I think it's Don", Conway once said.
He was born Thomas Conway in 1933 in the Cleveland suburb of Willoughby.