In 1972, Teaff was hired by Baylor University. Baylor originally hired Rudy Feldman from the University of New Mexico, but Feldman quit after one day, leaving the job to Teaff. The Baylor football team had been 7–43–1 in the five seasons preceding Teaff's arrival. Teaff quickly built Baylor into a competitive team and in 1974, Baylor won eight games and captured the Southwest Conference title for the first time since 1924. In the process they defeated the Texas Longhorns, 34–24, after rallying from a 24–7 halftime deficit. It was Baylor's first victory over Texas in 17 years. The 1974 season and the win over Texas are commonly referred to as the "Miracle on the Brazos," named after the Brazos River near the Baylor campus.