A crafty right-handed pitcher, Brewer was a two-year letterman in both baseball and football at Pasadena High School during the 1960s. He was part of the Eagles' district-champion baseball team his junior year, and as a senior, he posted a 4-0 record in district play. He continued his baseball career at San Jacinto College for two seasons before transferring to the University of Houston.

As a key pitcher for the Cougars in 1966 and 1967, Brewer delivered a scoreless extra-inning relief effort against Boston College during the 1967 College World Series and later pitched a four-hit shutout against Arizona State, propelling U of H into the championship game. His career 2.00 ERA ranks third in school history, and his .800 winning percentage (8-2) is fourth.

After college, Brewer served in the Air Force in Vietnam and retired as a full colonel. He was inducted into the University of Houston's Athletics Hall of Honor in 2024.