Brandon attended Nacogdoches High School in Texas and was signed as a free agent in 1959 by the Pittsburgh Pirates.

In 1966, his rookie season, he made 40 appearances (17 starts) for Boston and finished 8–8 with a 3.31 ERA, a career-high 101 strikeouts, five complete games and two shutouts.

[1] On July 20, 1966, Brandon tossed a complete game, allowing one earned run on just two hits in a win over the California Angels.

[2] However, Brandon developed arm problems at this early stage of his career and slumped to a 5–11 record in 1967, then pitched only 12+2⁄3 innings in 1968.

[1] A year later, he divided his playing time between the expansion Seattle Pilots and Minnesota, and then spent the entire 1970 season with the Triple-A Tucson Toros, in the Chicago White Sox farm system.