Wyatt's most notable victory at Tennessee came on November 7, 1959, when the 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 as both a player and a coach.
Wyatt married Mary Alson Miller in about 1940, and they had one daughter named Mary Gail "Missy" in 1942.