Wyatt's most notable victory at Tennessee came on November 7, 1959, when his Tennessee Volunteers football Volunteers upset top-ranked LSU, 14–13, by stopping a two-point conversion attempt by eventual Heisman Trophy winner Billy Cannon late in the game. The victory ended the Tigers' 18-game winning streak. Wyatt was elected to the College Football Hall of Fame in 1972 as a player and again in 1997 as a coach. Wyatt married Mary Alson Miller in about 1940, and they had one daughter named Mary Gail "Missy" in 1942.