Schnellenberger graduated from Flaget High School in Louisville, Kentucky, where he played football, basketball and baseball before earning a scholarship to the University of Kentucky. Schnellenberger was an All-American tight end at Kentucky and worked as an assistant coach there under head coach Blanton Collier. There he joined the Pi Kappa Alpha Fraternity. Schnellenberger also served as offensive coordinator under his college coach Bear Bryant at Alabama, helping Alabama to win three national championships in 1961, 1964 and 1965 before leaving in 1966 to take a job in the NFL as offensive coordinator of the Los Angeles Rams under George Allen, then being hired by Don Shula in 1970 to become the offensive coordinator for the Miami Dolphins and parlaying the success of Miami's 1972 perfect season into becoming the new head coach of the Baltimore Colts in 1973.
Schnellenberger's Colts went 4-10 in his one full season but managed to pull an upset on the heavily favored Dolphins towards the end of the 1973 season. After the Colts started the 1974 season 0-3, Schnellenberger was fired and replaced by Joe Thomas. He returned to the Dolphins coaching staff the following year and remained there until being offered the head coaching job at the University of Miami.