In August 1969, Zepp was called up by the Twins and made his major league debut on August 12, 1969. In four games for the Twins at the waning months of the 1969 season, he compiled a 6.75 ERA in 5-1/3 innings pitched. In 1970, Zepp appeared in 43 games, including 20 games as a starter, compiling a 9–4 record and a 3.22 ERA. He also ranked third in the American League having hit batsmen nine times in 1970. Zepp made two short relief appearances in the 1970 American League Championship Series against the Baltimore Orioles, giving up two hits and one run in one inning.