Nicknamed "Soup" because of his last name, Campbell was one of the top relief pitchers in all of baseball with the Twins in 1976 and the Red Sox in 1977. He signed with Boston after the 1976 season as one of the first high profile big money free agents in baseball. Campbell was elected to the American League all-star team in 1977. Campbell was awarded both AL Fireman of the Year by The Sporting News and Rolaids Relief Man of the Year Award (the first American League winner and first two-time winner of this award) following the 1976 and 1977 campaigns. Campbell is tied for the American League record for wins by a reliever in a single season, as a result of his 17–5 performance in 1976.
He began experiencing arm trouble in 1978, and never again regained his once dominant status in the game.