A dominant right-handed pitcher for Missouri Baptist College in the late 1970s and early 1980s. He was the top pitcher on his team in 1981 with 45 strikeouts and a 1.78 ERA. In 1980, Tiefenthaler was a pitcher for East Central College in Union, Missouri. He pitched for the C&H Travelers in 1980 and 1981. The Travelers won the Metro-Collegiate League championship with Randy on the mound closing out the title game in 1980. That year, the Travelers were a perfect 25-0.

From 1979-87, he pitched for Old Monroe in the Eastern Missouri Baseball Association. In 1979, he spun a no-hitter against Flint Hill and in 1985, he had eight consecutive complete game victories en route to the EMBA Little World Series.

In later years, Tiefenthaler was a pitcher in the St. Louis Baseball Forever League, which is an affiliate of the Roy Hobbs Baseball League.

In the 1970s, he pitched for the Wentzville American Legion Post 323, and Troy Buchanan High School in Troy, Missouri. For many years, Randy has been involved with the Troy American Legion Post 94.

In 1998, he helped found the Moscow Mills Athletic Association. He served as board chairman from 2002-2004. He has actively supported both the Metro-Collegiate League and the St. Louis Amateur Baseball Association.