Stovall was a catcher in the farm system of the Minnesota Twins in the 1970s. He played for the Elizabethton Twins in Tennessee.

From 1980 to 1994, he caught for the Colt 45s in the Mon-Clair League, helping his team win the St. Clair Division title in 1990. During his 15 seasons with the Colt 45s, his composite batting average was well over .300.

He also played for East St. Louis in the Mon-Clair League, helping his club to second-place finishes in 1979 and 1981. In 1991, Stovall and his son, DaRond Stovall, both played on the East St. Louis team. DaRond went on to play in the Major Leagues with the Montreal Expos.

In the 1970s, Stovall was a catcher for East St. Louis High School and Greenville (Illinois) College. Don played in the Tandy League in the 1990s.

Stovall is still active as a player in the St. Louis Baseball Forever League. He has been a catcher for the Pirates, Wildcats, Badgers, Sharks, and Game Face. He has coached high school baseball for the past 25 years. In 2020, Stovall was inducted into the National Semi-Pro Baseball Hall of Fame.