Dunn, a Memphis dentist before he got into politics, was a surprise choice for the Republican nomination for governor in 1970. He defeated John Jay Hooker in the election that year as white voters in Memphis and Tennessee abandoned the Democratic Party in large numbers. He served from 1971 until 1975. Tennessee governors were only allowed to serve one term at that time.
Dunn, a former chairman of the Shelby County Republican Party, was the first Republican elected governor of Tennessee in 50 years. He went into business in Nashville following his term.