Cormac McCarthy, one of the primo American novelists of the late 20th century. I know, I know, he’s still working and won his Pulitzer in 2006 but the bulk of his work is 20th century.
Sticking with Knoxville but outside the halls of old UT, there are fellow Pulitzer winners James Agee and Alex Haley (who had an adjunct professorship at UT for a bit). And there’s Frances Hodgson Burnett, author of The Secret Garden and Little Lord Fauntleroy. And one I like a lot but not many seem to know is George Washington Harris, author of the Sut Lovingood stories of the mid 19th century (really funny stuff).
Oh, and don’t forget Lowell Cunningham, the comic book writer who created Men In Black, who is a UT alum.