Born in Detroit, Zepp was a "superstar" in high school but decided to attend college at the University of Michigan, "where he lost his velocity and confidence." (Patrick Harrigan, "The Detroit Tigers: Club and Community 1945-1995" (Univ. Toronto Press 1997), p. 129. He was drafted but did not sign on three occasions while attending school: 1965 by the Milwaukee Braves, 1966 by the Detroit Tigers, and 1967 by the Boston Red Sox.
He was ultimately signed by the Minnesota Twins as an amateur free agent in 1968. He played for the Twins in 1969 and 1970, appearing in 47 games. In 1970, he was 9-4 for the Twins in 43 games, including 20 as a starter. His 1969 ERA was 3.22, well below the league average for an Adjusted ERA+ of 116. He was also No. 3 in the American League having hit batsmen 9 times in 1970. Zepp made two short relief appearnaces in the 1970 American League Championship Series against the Orioles, giving up 2 hits and 1 run in 1 inning.
Zepp was traded to the Detroit Tigers in March 1971 and played in 16 games for the 1971 Tigers. His ERA ballooned to 5.12 in 1971, and he played his last major league game on June 20, 1971. Zepp later recalled that he suffered a "Tommy John injury," tearing a tendon and resulting in lost arm strength. Zepp decided not to undergo risky surgery and instead retired from baseball. (Patrick Harrigan, "The Detroit Tigers: Club and Community 1945-1995," p. 135.)