Vowell played mostly at end and was a member of the 1914SIAA champion Vols; the program's first championship of any kind. He scored three touchdowns in that season's final game against Kentucky.
Vowell scored the winning touchdown in the victory over Vanderbilt in 1916 immediately dubbed the upset of the season. He was selected All-Southern in 1916, a year in which he was captain and helped lead the Volunteers to an 8–0–1 record and a share of the SIAA championship. Walter Camp placed Vowell on his All-America third-team. His older brother Morris Vowell was a tackle on some of the same teams. Graham and his family worked in the lumber business.
1921
Vowell came back in 1921, and was given a gold watch by Knoxville fans.