During his senior year at Mississippi, Gibbs led the Ole Miss Rebels football team to a 10–0–1 record, with the lone blemish a 6-6 deadlock against an inferior LSU squad (the Tigers went 5-4-1 after winning 20 of 22 games in 1958 and 1959) at Oxford, Mississippi. The Rebels won the 1961 Sugar Bowl, defeating the Rice Owls football team 14-6, as Gibbs scored both touchdowns. The Rebels were recognized as national champions by the Football Writers Association of America. Gibbs was named to the 1960 College Football All-America Team. That year, he was also named SEC Player of the Year.