Perkins attended the University of Alabama, playing football 1964-1966. He played for the legendary coach Bear Bryant and was a teammate of Pro Football Hall of Fame quarterback Joe Namath. The Crimson Tide won national championships in both 1964 and 1965, and Southeastern Conference championships in 1964, 1965, and 1966. During his senior year, he was named team captain. He was also selected as an All-American in 1966.

Perkins became head coach at his alma mater, the University of Alabama, for four years from 1983-1986, compiling a record of 32-15-1 and winning three bowl games, but the other season had a losing record. It was the first losing season at Alabama since 1957. He has the distinction of being the only head coach to lead Alabama to a victory over the Fighting Irish of Notre Dame.